Author: Dihua Jiang
Publisher: American Mathematical Society
ISBN: 1470469073
Category : Mathematics
Languages : en
Pages : 104
Book Description
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Harmonic Analysis and Gamma Functions on Symplectic Groups
Author: Dihua Jiang
Publisher: American Mathematical Society
ISBN: 1470469073
Category : Mathematics
Languages : en
Pages : 104
Book Description
View the abstract.
Publisher: American Mathematical Society
ISBN: 1470469073
Category : Mathematics
Languages : en
Pages : 104
Book Description
View the abstract.
Symplectic Methods in Harmonic Analysis and in Mathematical Physics
Author: Maurice A. de Gosson
Publisher: Springer Science & Business Media
ISBN: 3764399929
Category : Mathematics
Languages : en
Pages : 351
Book Description
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 where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. 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.
Publisher: Springer Science & Business Media
ISBN: 3764399929
Category : Mathematics
Languages : en
Pages : 351
Book Description
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 where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. 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.
Harmonic and Applied Analysis
Author: Stephan Dahlke
Publisher: Birkhäuser
ISBN: 3319188631
Category : Mathematics
Languages : en
Pages : 268
Book Description
This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.
Publisher: Birkhäuser
ISBN: 3319188631
Category : Mathematics
Languages : en
Pages : 268
Book Description
This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.
On The Langlands Program: Endoscopy And Beyond
Author: Wee Teck Gan
Publisher: World Scientific
ISBN: 9811285837
Category : Mathematics
Languages : en
Pages : 449
Book Description
This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman-Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.
Publisher: World Scientific
ISBN: 9811285837
Category : Mathematics
Languages : en
Pages : 449
Book Description
This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman-Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.
Simple Supercuspidal $L$-Packets of Quasi-Split Classical Groups
Author: Masao Oi
Publisher: American Mathematical Society
ISBN: 1470469561
Category : Mathematics
Languages : en
Pages : 174
Book Description
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Publisher: American Mathematical Society
ISBN: 1470469561
Category : Mathematics
Languages : en
Pages : 174
Book Description
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Cubical Models of $(infty ,1)$-Categories
Author: Brandon Doherty
Publisher: American Mathematical Society
ISBN: 1470468948
Category : Mathematics
Languages : en
Pages : 122
Book Description
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Publisher: American Mathematical Society
ISBN: 1470468948
Category : Mathematics
Languages : en
Pages : 122
Book Description
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On Refined Conjectures of Birch and Swinnerton-Dyer Type for Hasse–Weil–Artin $L$-Series
Author: David Burns
Publisher: American Mathematical Society
ISBN: 1470469669
Category : Mathematics
Languages : en
Pages : 168
Book Description
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Publisher: American Mathematical Society
ISBN: 1470469669
Category : Mathematics
Languages : en
Pages : 168
Book Description
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A Plethora of Cluster Structures on $GL_n$
Author: M. Gekhtman
Publisher: American Mathematical Society
ISBN: 1470469707
Category : Mathematics
Languages : en
Pages : 116
Book Description
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Publisher: American Mathematical Society
ISBN: 1470469707
Category : Mathematics
Languages : en
Pages : 116
Book Description
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Stratified Noncommutative Geometry
Author: David Ayala
Publisher: American Mathematical Society
ISBN: 1470469626
Category : Mathematics
Languages : en
Pages : 272
Book Description
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Publisher: American Mathematical Society
ISBN: 1470469626
Category : Mathematics
Languages : en
Pages : 272
Book Description
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Harmonic Analysis and Hypergroups
Author: Ken Ross
Publisher: Springer Science & Business Media
ISBN: 0817643486
Category : Mathematics
Languages : en
Pages : 248
Book Description
An underlying theme in this text is the notion of hypergroups, the theory of which has been developed and used in fields as diverse as special functions, differential equations, probability theory, representation theory, measure theory, Hopf algebras, and quantum groups. Other topics include the harmonic analysis of analytic functions, ergodic theory and wavelets.
Publisher: Springer Science & Business Media
ISBN: 0817643486
Category : Mathematics
Languages : en
Pages : 248
Book Description
An underlying theme in this text is the notion of hypergroups, the theory of which has been developed and used in fields as diverse as special functions, differential equations, probability theory, representation theory, measure theory, Hopf algebras, and quantum groups. Other topics include the harmonic analysis of analytic functions, ergodic theory and wavelets.