Harmonic Analysis in Euclidean Spaces, Part 2 PDF Download
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Author: Guido Weiss
Publisher: American Mathematical Soc.
ISBN: 0821814389
Category : Mathematics
Languages : en
Pages : 448
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Book Description
Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.
Author: Guido Weiss
Publisher: American Mathematical Soc.
ISBN: 0821814389
Category : Mathematics
Languages : en
Pages : 448
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Book Description
Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.
Author: Guido Weiss
Publisher:
ISBN:
Category :
Languages : en
Pages : 438
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Book Description
Author: Guido L. Weiss
Publisher: American Mathematical Soc.
ISBN: 9780821867945
Category : Mathematics
Languages : en
Pages : 492
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Book Description
Contains sections on Real harmonic analysis, Hardy spaces and BMO,Harmonic functions, potential theory and theory of functions of one complex variable
Author: Guido Weiss
Publisher: American Mathematical Soc.
ISBN: 0821814362
Category : Generalized spaces
Languages : en
Pages : 488
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Book Description
Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 140088389X
Category : Mathematics
Languages : en
Pages : 312
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Book Description
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Author: Isaac Pesenson
Publisher: Birkhäuser
ISBN: 3319555561
Category : Mathematics
Languages : en
Pages : 510
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Book Description
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Author: Kenneth Hoffman
Publisher: Courier Dover Publications
ISBN: 0486841413
Category : Mathematics
Languages : en
Pages : 449
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Book Description
Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.
Author: Guido Weiss
Publisher:
ISBN:
Category :
Languages : en
Pages : 460
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Book Description
Author: J. J. Benedetto
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Some analytic problems related to statistical mechanics; On spectral synthesis in IRn, n . 2; Fourier analysis of multilinear convolutions, Calderon's theorem, and analysis on Lipschitz curves; The complex method for interpolation of operators acting on families of Banach spaces; Maximal functions.
Author: Audrey Terras
Publisher: Springer Science & Business Media
ISBN: 146147972X
Category : Mathematics
Languages : en
Pages : 430
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Book Description
This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.
