Discrete Fourier Analysis / Wong, M. W (2011)  

Público ISBD Título : Discrete Fourier Analysis Tipo de documento: documento electrónico Autores: Wong, M. W ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2011 Colección: Pseudo-Differential Operators, Theory and Applications num. 5 Número de páginas: VIII, 177 p. 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-0348-0116-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Harmonic  analysis  Fourier  Partial  differential  equations  Numerical  Analysis  Abstract  Differential  Equations Clasificación: 51 Matemáticas Resumen: This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis.   The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis.   Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study Nota de contenido: Preface -- The Finite Fourier Transform -- Translation-Invariant Linear Operators -- Circulant Matrices -- Convolution Operators -- Fourier Multipliers -- Eigenvalues and Eigenfunctions -- The Fast Fourier Transform -- Time-Frequency Analysis -- Time-Frequency Localized Bases -- Wavelet Transforms and Filter Banks -- Haar Wavelets -- Daubechies Wavelets -- The Trace -- Hilbert Spaces -- Bounded Linear Operators -- Self-Adjoint Operators -- Compact Operators -- The Spectral Theorem -- Schatten–von Neumann Classes -- Fourier Series -- Fourier Multipliers on S1 -- Pseudo-Differential Operators on S1 -- Pseudo-Differential Operators on Z -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0116-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33266 Discrete Fourier Analysis [documento electrónico] / Wong, M. W ; SpringerLink (Online service) . - Basel : Springer Basel, 2011 . - VIII, 177 p. 1 illus. in color : online resource. - (Pseudo-Differential Operators, Theory and Applications; 5) . ISBN : 978-3-0348-0116-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Harmonic  analysis  Fourier  Partial  differential  equations  Numerical  Analysis  Abstract  Differential  Equations Clasificación: 51 Matemáticas Resumen: This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis.   The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis.   Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study Nota de contenido: Preface -- The Finite Fourier Transform -- Translation-Invariant Linear Operators -- Circulant Matrices -- Convolution Operators -- Fourier Multipliers -- Eigenvalues and Eigenfunctions -- The Fast Fourier Transform -- Time-Frequency Analysis -- Time-Frequency Localized Bases -- Wavelet Transforms and Filter Banks -- Haar Wavelets -- Daubechies Wavelets -- The Trace -- Hilbert Spaces -- Bounded Linear Operators -- Self-Adjoint Operators -- Compact Operators -- The Spectral Theorem -- Schatten–von Neumann Classes -- Fourier Series -- Fourier Multipliers on S1 -- Pseudo-Differential Operators on S1 -- Pseudo-Differential Operators on Z -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0116-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33266

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Functional Analysis Methods for Reliability Models / Gupur, Geni (2011)  

Público ISBD Título : Functional Analysis Methods for Reliability Models Tipo de documento: documento electrónico Autores: Gupur, Geni ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2011 Colección: Pseudo-Differential Operators, Theory and Applications num. 6 Número de páginas: VIII, 277 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0101-0 Idioma : Inglés (eng) Palabras clave: Mathematics  Functional  analysis  Operations  research  Management  science  Research,  Science  Analysis Clasificación: 51 Matemáticas Resumen: The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key importance – schedule delays, inconvenience, customer dissatisfaction, and loss of prestige and even weakening of national security are common examples of results that are caused by unreliability of systems and individuals. The book begins with an introduction to C0-semigroup theory. Then, after a brief history of reliability theory, methods that study the well-posedness, the asymptotic behaviors of solutions and reliability indices for varied reliability models are presented. Finally, further research problems are explored. Functional Analysis Methods for Reliability Models is an excellent reference for graduate students and researchers in operations research, applied mathematics and systems engineering Nota de contenido: Preface -- C0-Semigroup of Linear Operators and Cauchy Problems -- Statement of the Problems -- The System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity -- Transfer Line Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Infinite Capacity -- Further Research Problems -- Bibliography En línea: http://dx.doi.org/10.1007/978-3-0348-0101-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33261 Functional Analysis Methods for Reliability Models [documento electrónico] / Gupur, Geni ; SpringerLink (Online service) . - Basel : Springer Basel, 2011 . - VIII, 277 p : online resource. - (Pseudo-Differential Operators, Theory and Applications; 6) . ISBN : 978-3-0348-0101-0 Idioma : Inglés (eng) Palabras clave: Mathematics  Functional  analysis  Operations  research  Management  science  Research,  Science  Analysis Clasificación: 51 Matemáticas Resumen: The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key importance – schedule delays, inconvenience, customer dissatisfaction, and loss of prestige and even weakening of national security are common examples of results that are caused by unreliability of systems and individuals. The book begins with an introduction to C0-semigroup theory. Then, after a brief history of reliability theory, methods that study the well-posedness, the asymptotic behaviors of solutions and reliability indices for varied reliability models are presented. Finally, further research problems are explored. Functional Analysis Methods for Reliability Models is an excellent reference for graduate students and researchers in operations research, applied mathematics and systems engineering Nota de contenido: Preface -- C0-Semigroup of Linear Operators and Cauchy Problems -- Statement of the Problems -- The System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity -- Transfer Line Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Infinite Capacity -- Further Research Problems -- Bibliography En línea: http://dx.doi.org/10.1007/978-3-0348-0101-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33261

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Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms / Unterberger, André (2011)  

Público ISBD Título : Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms Tipo de documento: documento electrónico Autores: Unterberger, André ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2011 Colección: Pseudo-Differential Operators, Theory and Applications num. 8 Número de páginas: VIII, 300p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0166-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Operator  theory  Number  Theory Clasificación: 51 Matemáticas Resumen: Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane ? to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in ? according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g Î SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On ?, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis Nota de contenido: Introduction -- The Weyl calculus -- The Radon transformation and applications -- Automorphic functions and automorphic distributions -- A class of Poincaré series -- Spectral decomposition of the Poincaré summation process -- The totally radial Weyl calculus and arithmetic -- Should one generalize the Weyl calculus to an adelic setting? -- Index of notation -- Subject Index -- Bibliography En línea: http://dx.doi.org/10.1007/978-3-0348-0166-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33272 Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms [documento electrónico] / Unterberger, André ; SpringerLink (Online service) . - Basel : Springer Basel, 2011 . - VIII, 300p : online resource. - (Pseudo-Differential Operators, Theory and Applications; 8) . ISBN : 978-3-0348-0166-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Operator  theory  Number  Theory Clasificación: 51 Matemáticas Resumen: Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane ? to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in ? according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g Î SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On ?, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis Nota de contenido: Introduction -- The Weyl calculus -- The Radon transformation and applications -- Automorphic functions and automorphic distributions -- A class of Poincaré series -- Spectral decomposition of the Poincaré summation process -- The totally radial Weyl calculus and arithmetic -- Should one generalize the Weyl calculus to an adelic setting? -- Index of notation -- Subject Index -- Bibliography En línea: http://dx.doi.org/10.1007/978-3-0348-0166-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33272

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Symplectic Methods in Harmonic Analysis and in Mathematical Physics / Gosson, Maurice A. de (2011)  

Público ISBD Título : Symplectic Methods in Harmonic Analysis and in Mathematical Physics Tipo de documento: documento electrónico Autores: Gosson, Maurice A. de ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2011 Colección: Pseudo-Differential Operators, Theory and Applications num. 7 Número de páginas: XXIV, 338 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-9992-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Operator  theory  Partial  differential  equations  Differential  geometry  Mathematical  physics  Theory  Equations  Physics  Geometry Clasificación: 51 Matemáticas Resumen: The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space is introduced and studied, where the main role is played by “Bopp operators” (also called “Landau operators” in the literature). This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references En línea: http://dx.doi.org/10.1007/978-3-7643-9992-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33444 Symplectic Methods in Harmonic Analysis and in Mathematical Physics [documento electrónico] / Gosson, Maurice A. de ; SpringerLink (Online service) . - Basel : Springer Basel, 2011 . - XXIV, 338 p : online resource. - (Pseudo-Differential Operators, Theory and Applications; 7) . ISBN : 978-3-7643-9992-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Operator  theory  Partial  differential  equations  Differential  geometry  Mathematical  physics  Theory  Equations  Physics  Geometry Clasificación: 51 Matemáticas Resumen: The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space is introduced and studied, where the main role is played by “Bopp operators” (also called “Landau operators” in the literature). This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references En línea: http://dx.doi.org/10.1007/978-3-7643-9992-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33444

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The Weyl Operator and its Generalization / Cohen, Leon (2013)  

Público ISBD Título : The Weyl Operator and its Generalization Tipo de documento: documento electrónico Autores: Cohen, Leon ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Pseudo-Differential Operators, Theory and Applications num. 9 Número de páginas: XII, 159 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0294-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Operator  theory  Partial  differential  equations  Mathematical  physics  Differential  Equations  Theory  Physics Clasificación: 51 Matemáticas Resumen: This book deals with the theory and application of associating a function of two variables with a function of two operators that do not commute. The concept of associating ordinary functions with operators has arisen in many areas of science and mathematics, and up to the beginning of the twentieth century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generally being the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that do not commute. Methods to do so became known as rules of association, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it was realized that for every correspondence rule there is a corresponding phase-space distribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the field of time-frequency analysis where the aim is to understand signals with changing frequencies. The Weyl Operator and Its Generalization aims at bringing together the basic results of the field in a unified manner. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner Nota de contenido: Introduction -- The Fundamental Idea, Terminology, and Operator Algebra -- The Weyl Operator -- The Algebra of the Weyl Operator -- Product of Operators, Commutators, and the Moyal Sin Bracket -- Some Other Ordering Rules -- Generalized Operator Association -- The Fourier, Monomial, and Delta Function Associations -- Transformation Between Associations -- Path Integral Approach -- The Distribution of a Symbol and Operator -- The Uncertainty Principle -- Phase-Space Distributions -- Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform -- Time - Frequency Analysis -- The Transformation of Differential Equations into Phase Space -- The Representation of Functions -- The N Operator Case En línea: http://dx.doi.org/10.1007/978-3-0348-0294-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32411 The Weyl Operator and its Generalization [documento electrónico] / Cohen, Leon ; SpringerLink (Online service) . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - XII, 159 p : online resource. - (Pseudo-Differential Operators, Theory and Applications; 9) . ISBN : 978-3-0348-0294-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Operator  theory  Partial  differential  equations  Mathematical  physics  Differential  Equations  Theory  Physics Clasificación: 51 Matemáticas Resumen: This book deals with the theory and application of associating a function of two variables with a function of two operators that do not commute. The concept of associating ordinary functions with operators has arisen in many areas of science and mathematics, and up to the beginning of the twentieth century many isolated results were obtained. These developments were mostly based on associating a function of one variable with one operator, the operator generally being the differentiation operator. With the discovery of quantum mechanics in the years 1925-1930, there arose, in a natural way, the issue that one has to associate a function of two variables with a function of two operators that do not commute. Methods to do so became known as rules of association, correspondence rules, or ordering rules. This has led to a wonderfully rich mathematical development that has found applications in many fields. Subsequently it was realized that for every correspondence rule there is a corresponding phase-space distribution. Now the fields of correspondence rules and phase-space distributions are intimately connected. A similar development occurred in the field of time-frequency analysis where the aim is to understand signals with changing frequencies. The Weyl Operator and Its Generalization aims at bringing together the basic results of the field in a unified manner. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner Nota de contenido: Introduction -- The Fundamental Idea, Terminology, and Operator Algebra -- The Weyl Operator -- The Algebra of the Weyl Operator -- Product of Operators, Commutators, and the Moyal Sin Bracket -- Some Other Ordering Rules -- Generalized Operator Association -- The Fourier, Monomial, and Delta Function Associations -- Transformation Between Associations -- Path Integral Approach -- The Distribution of a Symbol and Operator -- The Uncertainty Principle -- Phase-Space Distributions -- Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform -- Time - Frequency Analysis -- The Transformation of Differential Equations into Phase Space -- The Representation of Functions -- The N Operator Case En línea: http://dx.doi.org/10.1007/978-3-0348-0294-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32411

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