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Título : Integral Geometry and Radon Transforms Tipo de documento: documento electrónico Autores: Sigurdur Helgason ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Número de páginas: XIII, 301 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-6055-9 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Integral transforms Operational calculus Differential geometry Geometry Transforms, Calculus Analysis and on Groups, Groups Clasificación: 51 Matemáticas Resumen: In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book is concentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University Nota de contenido: The Radon Transformon Rn -- A Duality in Integral Geometry -- The Radon Transform on Two-Point Homogeneous Spaces -- The X-Ray Transform on a Symmetric Space -- Orbital Integrals -- The Mean-Value Operator -- Fourier Transforms and Distribution: A Rapid Course -- Lie Transformation Groups and Differential Operators -- Bibliography -- Notational Conventions -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-6055-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33145 Integral Geometry and Radon Transforms [documento electrónico] / Sigurdur Helgason ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XIII, 301 p : online resource.
ISBN : 978-1-4419-6055-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Integral transforms Operational calculus Differential geometry Geometry Transforms, Calculus Analysis and on Groups, Groups Clasificación: 51 Matemáticas Resumen: In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book is concentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University Nota de contenido: The Radon Transformon Rn -- A Duality in Integral Geometry -- The Radon Transform on Two-Point Homogeneous Spaces -- The X-Ray Transform on a Symmetric Space -- Orbital Integrals -- The Mean-Value Operator -- Fourier Transforms and Distribution: A Rapid Course -- Lie Transformation Groups and Differential Operators -- Bibliography -- Notational Conventions -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-6055-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33145 Ejemplares
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Título : Introduction to Hyperfunctions and Their Integral Transforms : An Applied and Computational Approach Tipo de documento: documento electrónico Autores: Urs Graf ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2010 Número de páginas: 432 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0408-6 Idioma : Inglés (eng) Palabras clave: Mathematics Fourier analysis Integral transforms Operational calculus Special functions Computer mathematics Transforms, Calculus Functions Computational Science and Engineering Analysis Clasificación: 51 Matemáticas Resumen: This textbook presents an elementary introduction to generalized functions by using Sato's approach of hyperfunctions which is based on complex function theory. This very intuitive and appealing approach has particularly great computational power. The concept of hyperfunctions and their analytic properties is introduced and discussed in detail in the first two chapters of the book. Thereafter the focus lies on generalizing the (classical) Laplace, Fourier, Hilbert, Mellin, and Hankel transformations to hyperfunctions. Applications to integral and differential equations and a rich variety of concrete examples accompany the text throughout the book. Requiring only standard knowledge of the theory of complex variables, the material is easily accessible for advanced undergraduate or graduate students. It serves as well as a reference for researchers in pure and applied mathematics, engineering and physics. Nota de contenido: to Hyperfunctions -- Analytic Properties -- Laplace Transforms -- Fourier Transforms -- Hilbert Transforms -- Mellin Transforms -- Hankel Transforms En línea: http://dx.doi.org/10.1007/978-3-0346-0408-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33678 Introduction to Hyperfunctions and Their Integral Transforms : An Applied and Computational Approach [documento electrónico] / Urs Graf ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2010 . - 432 p : online resource.
ISBN : 978-3-0346-0408-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Fourier analysis Integral transforms Operational calculus Special functions Computer mathematics Transforms, Calculus Functions Computational Science and Engineering Analysis Clasificación: 51 Matemáticas Resumen: This textbook presents an elementary introduction to generalized functions by using Sato's approach of hyperfunctions which is based on complex function theory. This very intuitive and appealing approach has particularly great computational power. The concept of hyperfunctions and their analytic properties is introduced and discussed in detail in the first two chapters of the book. Thereafter the focus lies on generalizing the (classical) Laplace, Fourier, Hilbert, Mellin, and Hankel transformations to hyperfunctions. Applications to integral and differential equations and a rich variety of concrete examples accompany the text throughout the book. Requiring only standard knowledge of the theory of complex variables, the material is easily accessible for advanced undergraduate or graduate students. It serves as well as a reference for researchers in pure and applied mathematics, engineering and physics. Nota de contenido: to Hyperfunctions -- Analytic Properties -- Laplace Transforms -- Fourier Transforms -- Hilbert Transforms -- Mellin Transforms -- Hankel Transforms En línea: http://dx.doi.org/10.1007/978-3-0346-0408-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33678 Ejemplares
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Título : Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Takashi Aoki ; Hideyuki Majima ; Yoshitsugu Takei ; Nobuyuki Tose Editorial: Tokyo : Springer Japan Fecha de publicación: 2008 Número de páginas: XVII, 352 p Il.: online resource ISBN/ISSN/DL: 978-4-431-73240-2 Idioma : Inglés (eng) Palabras clave: Mathematics Integral transforms Operational calculus Differential equations Partial differential Special functions Transforms, Calculus Ordinary Equations Functions Clasificación: 51 Matemáticas Nota de contenido: The work of T. Kawai -- Publications of Professor Takahiro Kawai -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on exact WKB analysis -- Contributed papers -- Virtual turning points — A gift of microlocal analysis to the exact WKB analysis -- Regular sequences associated with the Noumi-Yamada equations with a large parameter -- Ghost busting: Making sense of non-Hermitian Hamiltonians -- Vanishing of the logarithmic trace of generalized Szegö projectors -- Nonlinear Stokes phenomena in first or second order differential equations -- Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation -- Exact WKB analysis near a simple turning point -- The Borel transform -- On the use of Z-transforms in the summation of transseries for partial differential equations -- Some dynamical aspects of Painlevé VI -- An algebraic representation for correlation functions in integrable spin chains -- Inverse image of D-modules and quasi-b-functions -- The hypoelliptic Laplacian of J.-M. Bismut -- Commuting differential operators with regular singularities -- The behaviors of singular solutions of some partial differential equations in the complex domain -- Observations on the JWKB treatment of the quadratic barrier -- A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map -- Spectral instability for non-selfadjoint operators -- Boundary and lens rigidity, tensor tomography and analytic microlocal analysis -- Coupling of two partial differential equations and its application -- Instanton-type formal solutions for the first Painlevé hierarchy -- From exact-WKB toward singular quantum perturbation theory II -- WKB analysis and Poincaré theorem for vector fields En línea: http://dx.doi.org/10.1007/978-4-431-73240-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34431 Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai [documento electrónico] / SpringerLink (Online service) ; Takashi Aoki ; Hideyuki Majima ; Yoshitsugu Takei ; Nobuyuki Tose . - Tokyo : Springer Japan, 2008 . - XVII, 352 p : online resource.
ISBN : 978-4-431-73240-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral transforms Operational calculus Differential equations Partial differential Special functions Transforms, Calculus Ordinary Equations Functions Clasificación: 51 Matemáticas Nota de contenido: The work of T. Kawai -- Publications of Professor Takahiro Kawai -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on exact WKB analysis -- Contributed papers -- Virtual turning points — A gift of microlocal analysis to the exact WKB analysis -- Regular sequences associated with the Noumi-Yamada equations with a large parameter -- Ghost busting: Making sense of non-Hermitian Hamiltonians -- Vanishing of the logarithmic trace of generalized Szegö projectors -- Nonlinear Stokes phenomena in first or second order differential equations -- Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation -- Exact WKB analysis near a simple turning point -- The Borel transform -- On the use of Z-transforms in the summation of transseries for partial differential equations -- Some dynamical aspects of Painlevé VI -- An algebraic representation for correlation functions in integrable spin chains -- Inverse image of D-modules and quasi-b-functions -- The hypoelliptic Laplacian of J.-M. Bismut -- Commuting differential operators with regular singularities -- The behaviors of singular solutions of some partial differential equations in the complex domain -- Observations on the JWKB treatment of the quadratic barrier -- A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map -- Spectral instability for non-selfadjoint operators -- Boundary and lens rigidity, tensor tomography and analytic microlocal analysis -- Coupling of two partial differential equations and its application -- Instanton-type formal solutions for the first Painlevé hierarchy -- From exact-WKB toward singular quantum perturbation theory II -- WKB analysis and Poincaré theorem for vector fields En línea: http://dx.doi.org/10.1007/978-4-431-73240-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34431 Ejemplares
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Título : Offbeat Integral Geometry on Symmetric Spaces Tipo de documento: documento electrónico Autores: Valery V. Volchkov ; SpringerLink (Online service) ; Vitaly V. Volchkov Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Número de páginas: X, 592 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0572-8 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Integral transforms Operational calculus Special functions Differential geometry Functions Abstract Analysis Transforms, Calculus Geometry Clasificación: 51 Matemáticas Resumen: The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory Nota de contenido: Preface -- Part 1. Analysis on Symmetric Spaces. 1 Preliminaries -- 2 The Euclidean case -- 3 Symmetric spaces of the non-compact type.-4 Analogies for compact two-point homogeneous Spaces -- 5 The phase space associated to the Heisenberg group.-Part 2. Offbeat Integral Geometry -- 1 Functions with zero ball means on Euclidean space -- 2 Two-radii theorems in symmetric spaces -- 3 The problem of finding a function from its ball means -- 4 Sets with the Pompeiu property -- 5 Functions with zero integrals over polytopes.-6 Ellipsoidal means -- 7 The Pompeiu property on a sphere -- 8 The Pompeiu transform on symmetric spaces and groups.-9 Pompeiu transforms on manifolds -- Bibliography -- Index -- Basic notation En línea: http://dx.doi.org/10.1007/978-3-0348-0572-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32433 Offbeat Integral Geometry on Symmetric Spaces [documento electrónico] / Valery V. Volchkov ; SpringerLink (Online service) ; Vitaly V. Volchkov . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - X, 592 p : online resource.
ISBN : 978-3-0348-0572-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Integral transforms Operational calculus Special functions Differential geometry Functions Abstract Analysis Transforms, Calculus Geometry Clasificación: 51 Matemáticas Resumen: The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory Nota de contenido: Preface -- Part 1. Analysis on Symmetric Spaces. 1 Preliminaries -- 2 The Euclidean case -- 3 Symmetric spaces of the non-compact type.-4 Analogies for compact two-point homogeneous Spaces -- 5 The phase space associated to the Heisenberg group.-Part 2. Offbeat Integral Geometry -- 1 Functions with zero ball means on Euclidean space -- 2 Two-radii theorems in symmetric spaces -- 3 The problem of finding a function from its ball means -- 4 Sets with the Pompeiu property -- 5 Functions with zero integrals over polytopes.-6 Ellipsoidal means -- 7 The Pompeiu property on a sphere -- 8 The Pompeiu transform on symmetric spaces and groups.-9 Pompeiu transforms on manifolds -- Bibliography -- Index -- Basic notation En línea: http://dx.doi.org/10.1007/978-3-0348-0572-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32433 Ejemplares
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Título : Numerical Methods for Laplace Transform Inversion Tipo de documento: documento electrónico Autores: Alan M. Cohen ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2007 Colección: Numerical Methods and Algorithms, ISSN 1571-5698 num. 5 Número de páginas: XIV, 252 p. 25 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-68855-8 Idioma : Inglés (eng) Palabras clave: Mathematics Integral transforms Operational calculus Applied mathematics Engineering Transforms, Calculus Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Audience This book is intended for engineers, scientists, mathematicians, statisticians and financial planners Nota de contenido: Basic Results -- Inversion Formulae and Practical Results -- The Method of Series Expansion -- Quadrature Methods -- Rational Approximation Methods -- The Method of Talbot -- Methods based on the Post-Widder Inversion Formula -- The Method of Regularization -- Survey Results -- Applications En línea: http://dx.doi.org/10.1007/978-0-387-68855-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34510 Numerical Methods for Laplace Transform Inversion [documento electrónico] / Alan M. Cohen ; SpringerLink (Online service) . - Boston, MA : Springer US, 2007 . - XIV, 252 p. 25 illus : online resource. - (Numerical Methods and Algorithms, ISSN 1571-5698; 5) .
ISBN : 978-0-387-68855-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral transforms Operational calculus Applied mathematics Engineering Transforms, Calculus Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Audience This book is intended for engineers, scientists, mathematicians, statisticians and financial planners Nota de contenido: Basic Results -- Inversion Formulae and Practical Results -- The Method of Series Expansion -- Quadrature Methods -- Rational Approximation Methods -- The Method of Talbot -- Methods based on the Post-Widder Inversion Formula -- The Method of Regularization -- Survey Results -- Applications En línea: http://dx.doi.org/10.1007/978-0-387-68855-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34510 Ejemplares
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