Pointwise And Uniform Convergence Of Fourier Series On Su 2
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Pointwise And Uniform Convergence Of Fourier Series On Su 2
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Author : Donald Forrest Myers
language : en
Publisher:
Release Date : 2016
Pointwise And Uniform Convergence Of Fourier Series On Su 2 written by Donald Forrest Myers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Convergence categories.
"Let f be a Lipschitz function on the special unitary group SU(2). We prove that the Fourier partial sums of f converge to f uniformly on SU(2), thereby extending theorems of Caccioppoli, Mayer, and a special case of Ragozin. Pointwise convergence theorems for the Fourier series of functions on SU(2), due to Liu and Qian, were obtained by Clifford algebra techniques. We obtain similar versions of these theorems using simpler proof techniques: classical harmonic analysis and group theory"--Abstract, page iii.
Partial Differential Equations In Action
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Author : Sandro Salsa
language : en
Publisher: Springer Nature
Release Date : 2022-12-08
Partial Differential Equations In Action written by Sandro Salsa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-08 with Mathematics categories.
This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.
Representations Of Su 2 1 In Fourier Term Modules
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Author : Roelof W. Bruggeman
language : en
Publisher: Springer Nature
Release Date : 2023-11-06
Representations Of Su 2 1 In Fourier Term Modules written by Roelof W. Bruggeman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Mathematics categories.
This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
Understanding Mathematical Concepts In Physics
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Author : Sanjeev Dhurandhar
language : en
Publisher: Springer Nature
Release Date : 2024-07-16
Understanding Mathematical Concepts In Physics written by Sanjeev Dhurandhar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-16 with Science categories.
Modern mathematics has become an essential part of today’s physicist’s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy’s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of χ2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching.
Pseudo Differential Operators And Symmetries
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Author : Michael Ruzhansky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-29
Pseudo Differential Operators And Symmetries written by Michael Ruzhansky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-29 with Mathematics categories.
This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations
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Author : Radomir Stankovic
language : en
Publisher: Springer
Release Date : 2015-12-29
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations written by Radomir Stankovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-29 with Mathematics categories.
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2001
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The New Encyclop Dia Britannica Macrop Dia
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Author :
language : en
Publisher:
Release Date : 1993
The New Encyclop Dia Britannica Macrop Dia written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Encyclopedias and dictionaries categories.
This encyclopedia includes a two-volume index, a 12-volume Micropaedia (Ready reference), a 17-volume Macropaedia (Knowledge in depth), and the Propaedia.
Encyclopedia Of Physical Science And Technology
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Author :
language : en
Publisher:
Release Date : 2002
Encyclopedia Of Physical Science And Technology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Physical sciences categories.
Of the Encyclopedia of Physical Science and Technology: Has been completely updated with no less than 90% revised material and 50% new content throughout the volumes Presents eighteen volumes, nearly 800 authoritative articles and 14,500 pages Is lavishly illustrated with over 7,000 photographs, illustrations and tables Presents an increased emphasis on the hottest topics such as information processing, environmental science, biotechnology and biomedicine Includes a final Index Volume containing Thematic, Relational and Subject indexes.
The New Encyclop Dia Britannica Macrop Dia Knowledge In Depth
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Author :
language : en
Publisher:
Release Date : 2002
The New Encyclop Dia Britannica Macrop Dia Knowledge In Depth written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Encyclopedias and dictionaries categories.