Harmonic Analysis and Discrete Potential Theory
Harmonic Analysis and Discrete Potential Theory

Author: M.A. Picardello

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 299

ISBN-13: 1489923233

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This book collects the Proceedings of a Congress held in Frascati (Rome) in the period July 1 -July 10, 1991, on the subject of harmonic analysis and discrete potential theory, and related topics. The Congress was made possible by the financial support of the Italian National Research Council ("Gruppo GNAFA"), the Ministry of University ("Gruppo Analisi Funzionale" of the University of Milano), the University of Rome "Tor Vergata", and was also patronized by the Centro "Vito Volterra" of the University of Rome "Tor Vergata". Financial support for publishing these Proceedings was provided by the University of Rome "Tor Vergata", and by a generous contribution of the Centro "Vito Volterra". I am happy of this opportunity to acknowledge the generous support of all these Institutions, and to express my gratitude, and that of all the participants. A number of distinguished mathematicians took part in the Congress. Here is the list of participants: M. Babillot, F. Choucroun, Th. Coulhon, L. Elie, F. Ledrappier, N. Th. Varopoulos (Paris); L. Gallardo (Brest); Ph. Bougerol, B. Roynette (Nancy); O. Gebuhrer (Strasbourg); G. Ahumada-Bustamante (Mulhouse); A. Valette (Neuchatel); P. Gerl (Salzburg); W. Hansen, H. Leptin (Bielefeld); M. Bozejko, A. Hulanicki, T. Pytlik (Wroclaw); C. Thomassen (Lyngby); P. Sjogren (Goteborg); V. Kaimanovich (Leningrad); A. Nevo (Jerusalem); T. Steger (Chicago); S. Sawyer, M. Taibleson, G. Weiss (St. Louis); J. Cohen, S.S ali ani (Maryland); D. Voiculescu (Berkeley); A. Zemanian (Stony Brook); S. Northshield (Plattsburgh); J. Taylor (Montreal); J

Discrete Harmonic Analysis
Discrete Harmonic Analysis

Author: Tullio Ceccherini-Silberstein

Publisher: Cambridge University Press

Published: 2018-06-21

Total Pages: 589

ISBN-13: 1107182336

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A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

Potential Theory on Infinite Networks
Potential Theory on Infinite Networks

Author: Paolo M. Soardi

Publisher: Springer

Published: 2006-11-15

Total Pages: 199

ISBN-13: 3540487980

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The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Multiscale Potential Theory
Multiscale Potential Theory

Author: Willi Freeden

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 522

ISBN-13: 1461220483

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This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.

Potential Theory in Gravity and Magnetic Applications
Potential Theory in Gravity and Magnetic Applications

Author: Richard J. Blakely

Publisher: Cambridge University Press

Published: 1996-09-13

Total Pages: 468

ISBN-13: 9780521575478

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This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.

Random Walks and Discrete Potential Theory
Random Walks and Discrete Potential Theory

Author: M. Picardello

Publisher: Cambridge University Press

Published: 1999-11-18

Total Pages: 378

ISBN-13: 9780521773126

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Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.

Fourier Analysis on Number Fields
Fourier Analysis on Number Fields

Author: Dinakar Ramakrishnan

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 372

ISBN-13: 1475730853

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A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.

Classical and Multilinear Harmonic Analysis
Classical and Multilinear Harmonic Analysis

Author: Camil Muscalu

Publisher: Cambridge University Press

Published: 2013-01-31

Total Pages: 341

ISBN-13: 1107031826

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This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Harmonic Function Theory
Harmonic Function Theory

Author: Sheldon Axler

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 266

ISBN-13: 1475781377

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This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.

Harmonic Analysis for Engineers and Applied Scientists
Harmonic Analysis for Engineers and Applied Scientists

Author: Gregory S. Chirikjian

Publisher: Courier Dover Publications

Published: 2016-07-20

Total Pages: 881

ISBN-13: 0486795640

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Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.