Analysis and Probability Wavelets, Signals, Fractals / Palle E.T. Jorgensen (2006)  

Público ISBD Título : Analysis and Probability Wavelets, Signals, Fractals Tipo de documento: documento electrónico Autores: Palle E.T. Jorgensen ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 234 Número de páginas: XLVIII, 280 p Il.: online resource ISBN/ISSN/DL: 978-0-387-33082-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Applied  mathematics  Engineering  Information  theory  Probabilities  Probability  Theory  and  Stochastic  Processes  Applications  of  Appl.Mathematics/Computational  Methods  Signal,  Image  Speech  Processing  Communication,  Circuits Clasificación: 51 Matemáticas Resumen: This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals. The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications. Key features: • A hands-on approach for students, including tutorials and numerous exercises; • Excellent motivation throughout; • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics; • Includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations; • Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers; • Each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book. Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled Wavelets through a Looking Glass, ©2002 Birkhäuser Boston Nota de contenido: Introduction: Measures on path space -- Transition probabilities: Random walk -- ?o vs. ? -- A case study: Duality for Cantor sets -- Infinite products -- The minimal eigenfunction -- Generalizations and applications -- Pyramids and operators -- Pairs of representations of the Cuntz algebras , and their application to multiresolutions En línea: http://dx.doi.org/10.1007/978-0-387-33082-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34802 Analysis and Probability Wavelets, Signals, Fractals [documento electrónico] / Palle E.T. Jorgensen ; SpringerLink (Online service) . - New York, NY : Springer New York, 2006 . - XLVIII, 280 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 234) . ISBN : 978-0-387-33082-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Applied  mathematics  Engineering  Information  theory  Probabilities  Probability  Theory  and  Stochastic  Processes  Applications  of  Appl.Mathematics/Computational  Methods  Signal,  Image  Speech  Processing  Communication,  Circuits Clasificación: 51 Matemáticas Resumen: This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals. The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications. Key features: • A hands-on approach for students, including tutorials and numerous exercises; • Excellent motivation throughout; • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics; • Includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations; • Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers; • Each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book. Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled Wavelets through a Looking Glass, ©2002 Birkhäuser Boston Nota de contenido: Introduction: Measures on path space -- Transition probabilities: Random walk -- ?o vs. ? -- A case study: Duality for Cantor sets -- Infinite products -- The minimal eigenfunction -- Generalizations and applications -- Pyramids and operators -- Pairs of representations of the Cuntz algebras , and their application to multiresolutions En línea: http://dx.doi.org/10.1007/978-0-387-33082-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34802

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Representations, Wavelets, and Frames / SpringerLink (Online service) ; Palle E.T. Jorgensen ; Kathy D. Merrill ; Judith A. Packer (2008)  

Público ISBD Título : Representations, Wavelets, and Frames : A Celebration of the Mathematical Work of Lawrence W. Baggett Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Palle E.T. Jorgensen ; Kathy D. Merrill ; Judith A. Packer Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XL, 324 p. 22 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4683-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Harmonic  analysis  Fourier  Functional  Applied  mathematics  Engineering  Mathematical  models  Modeling  and  Industrial  Analysis  Signal,  Image  Speech  Processing  Abstract  Applications  of Clasificación: 51 Matemáticas Resumen: Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang Nota de contenido: Classical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett’s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression En línea: http://dx.doi.org/10.1007/978-0-8176-4683-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34277 Representations, Wavelets, and Frames : A Celebration of the Mathematical Work of Lawrence W. Baggett [documento electrónico] / SpringerLink (Online service) ; Palle E.T. Jorgensen ; Kathy D. Merrill ; Judith A. Packer . - Boston, MA : Birkhäuser Boston, 2008 . - XL, 324 p. 22 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) . ISBN : 978-0-8176-4683-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Harmonic  analysis  Fourier  Functional  Applied  mathematics  Engineering  Mathematical  models  Modeling  and  Industrial  Analysis  Signal,  Image  Speech  Processing  Abstract  Applications  of Clasificación: 51 Matemáticas Resumen: Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang Nota de contenido: Classical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett’s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression En línea: http://dx.doi.org/10.1007/978-0-8176-4683-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34277

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