Author: Yitzhak KatznelsonPublisher:
ISBN:
Category : Harmonic analysis
Languages : en
Pages : 292
Book Description
Author: Yitzhak KatznelsonIntroduction to Abstract Harmonic Analysis
Author: Lynn H. LoomisPublisher: Courier Corporation
ISBN: 0486481239
Category : Mathematics
Languages : en
Pages : 210
Book Description
"Harmonic analysis is a branch of advanced mathematics with applications in such diverse areas as signal processing, medical imaging, and quantum mechanics. This classic monograph is the work of a prominent contributor to the field. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition"--
A First Course in Harmonic Analysis
Author: Anton DeitmarPublisher: Springer Science & Business Media
ISBN: 147573834X
Category : Mathematics
Languages : en
Pages : 154
Book Description
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
An Introduction to Harmonic Analysis on Semisimple Lie Groups
Author: V. S. VaradarajanPublisher: Cambridge University Press
ISBN: 9780521663625
Category : Mathematics
Languages : en
Pages : 326
Book Description
Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.
Introduction to Harmonic Analysis and Generalized Gelfand Pairs
Author: Gerrit van DijkPublisher: Walter de Gruyter
ISBN: 3110220202
Category : Mathematics
Languages : en
Pages : 234
Book Description
This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs
Quantum Harmonic Analysis
Author: Maurice A. de GossonPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110722909
Category : Mathematics
Languages : en
Pages : 247
Book Description
Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Harmonic Analysis
Author: María Cristina PereyraPublisher: American Mathematical Soc.
ISBN: 0821875663
Category : Mathematics
Languages : en
Pages : 437
Book Description
Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
Principles of Harmonic Analysis
Author: Anton DeitmarPublisher: Springer
ISBN: 3319057928
Category : Mathematics
Languages : en
Pages : 330
Book Description
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
The Evolution of Applied Harmonic Analysis
Author: Elena PrestiniPublisher: Springer Science & Business Media
ISBN: 081768140X
Category : Mathematics
Languages : en
Pages : 366
Book Description
A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book, accessible to specialists and non-specialists, describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections. Historical sections interwoven with key scientific developments show how, when, where, and why harmonic analysis evolved "The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics.
