Harmonic Analysis And Rational Approximation

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Methods of Approximation Theory in Complex Analysis and Mathematical Physics

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Author : Andrei A. Gonchar
Publisher : Springer
ISBN 13 : 3540477926
Total Pages : 225 pages
Book Rating : 4.5/5 (44 download)

Book Synopsis Methods of Approximation Theory in Complex Analysis and Mathematical Physics by : Andrei A. Gonchar

Download or read book Methods of Approximation Theory in Complex Analysis and Mathematical Physics written by Andrei A. Gonchar and published by Springer. This book was released on 2008-01-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. Suslov: Classical Biorthogonal Rational Functions.- V.P. Havin, A. Presa Sague: Approximation properties of harmonic vector fields and differential forms.- O.G. Parfenov: Extremal problems for Blaschke products and N-widths.- A.J. Carpenter, R.S. Varga: Some Numerical Results on Best Uniform Polynomial Approximation of x on 0,1 .- J.S. Geronimo: Polynomials Orthogonal on the Unit Circle with Random Recurrence Coefficients.- S. Khrushchev: Parameters of orthogonal polynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.

Harmonic Analysis and Rational Approximation

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Author : Jean-Daniel Fournier
Publisher : Springer
ISBN 13 : 9783540818892
Total Pages : 311 pages
Book Rating : 4.8/5 (188 download)

Book Synopsis Harmonic Analysis and Rational Approximation by : Jean-Daniel Fournier

Download or read book Harmonic Analysis and Rational Approximation written by Jean-Daniel Fournier and published by Springer. This book was released on 2009-09-02 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book - an outgrowth of a topical summer school - sets out to introduce non-specialists from physics and engineering to the basic mathematical concepts of approximation and Fourier theory. After a general introduction, Part II of this volume contains basic material on the complex and harmonic analysis underlying the further developments presented. Part III deals with the essentials of approximation theory while Part IV completes the foundations by a tour of probability theory. Part V reviews some major applications in signal and control theory. In Part VI mathematical aspects of dynamical systems theory are discussed. Part VII, finally, is devoted to a modern approach to two physics problems: turbulence and the control and noise analysis in gravitational waves measurements.

Approximation Theory and Approximation Practice, Extended Edition

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Author : Lloyd N. Trefethen
Publisher : SIAM
ISBN 13 : 1611975948
Total Pages : 377 pages
Book Rating : 4.6/5 (119 download)

Book Synopsis Approximation Theory and Approximation Practice, Extended Edition by : Lloyd N. Trefethen

Download or read book Approximation Theory and Approximation Practice, Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.

Harmonic Analysis and Applications

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Author : John J. Benedetto
Publisher : CRC Press
ISBN 13 : 1000142213
Total Pages : 370 pages
Book Rating : 4.0/5 (1 download)

Book Synopsis Harmonic Analysis and Applications by : John J. Benedetto

Download or read book Harmonic Analysis and Applications written by John J. Benedetto and published by CRC Press. This book was released on 2020-12-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.

Complex Potential Theory

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Author : Paul M. Gauthier
Publisher : Springer Science & Business Media
ISBN 13 : 9401109346
Total Pages : 565 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis Complex Potential Theory by : Paul M. Gauthier

Download or read book Complex Potential Theory written by Paul M. Gauthier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993

A Simple Introduction to Numerical Analysis

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Author : R.D Harding
Publisher : CRC Press
ISBN 13 : 9780852741542
Total Pages : 190 pages
Book Rating : 4.7/5 (415 download)

Book Synopsis A Simple Introduction to Numerical Analysis by : R.D Harding

Download or read book A Simple Introduction to Numerical Analysis written by R.D Harding and published by CRC Press. This book was released on 1989-01-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation techniques are widely used in mathematics and applied physics, as exact solutions are frequently impossible to obtain. A Simple Introduction to Numerical Analysis, Volume 2: Interpolation and Approximation extends the first volume to consider problems in interpolation and approximation. Topics covered include the construction of interpolating functions, the determination of polynomial and rational function approximations, numerical quadrature, and the solution of boundary value problems in ordinary differential equations. As with the previous volume, the text is integrated with a software package that allows the reader to work through numerous examples. It is also possible to use the software to consider problems that are beyond the scope of the text. The authors' expertise in combining text and software has resulted in a very readable work.

Acta Numerica 1998: Volume 7

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Author : Arieh Iserles
Publisher : Cambridge University Press
ISBN 13 : 9780521643160
Total Pages : 388 pages
Book Rating : 4.6/5 (431 download)

Book Synopsis Acta Numerica 1998: Volume 7 by : Arieh Iserles

Download or read book Acta Numerica 1998: Volume 7 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1998-07-23 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual volume presenting substantive survey articles in numerical analysis and scientific computing.

The Convenient Setting of Global Analysis

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Author : Andreas Kriegl
Publisher : American Mathematical Society
ISBN 13 : 1470478935
Total Pages : 631 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis The Convenient Setting of Global Analysis by : Andreas Kriegl

Download or read book The Convenient Setting of Global Analysis written by Andreas Kriegl and published by American Mathematical Society. This book was released on 2024-08-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.

Explorations in Harmonic Analysis

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Author : Steven G. Krantz
Publisher : Springer Science & Business Media
ISBN 13 : 0817646698
Total Pages : 367 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Explorations in Harmonic Analysis by : Steven G. Krantz

Download or read book Explorations in Harmonic Analysis written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2009-05-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

50 Years with Hardy Spaces

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Author : Anton Baranov
Publisher : Birkhäuser
ISBN 13 : 3319590782
Total Pages : 477 pages
Book Rating : 4.3/5 (195 download)

Book Synopsis 50 Years with Hardy Spaces by : Anton Baranov

Download or read book 50 Years with Hardy Spaces written by Anton Baranov and published by Birkhäuser. This book was released on 2018-03-28 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.

Current Trends in Operator Theory and its Applications

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Author : Joseph A. Ball
Publisher : Birkhäuser
ISBN 13 : 3034878818
Total Pages : 604 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Current Trends in Operator Theory and its Applications by : Joseph A. Ball

Download or read book Current Trends in Operator Theory and its Applications written by Joseph A. Ball and published by Birkhäuser. This book was released on 2012-12-06 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

Arithmetic of Higher-Dimensional Algebraic Varieties

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Author : Bjorn Poonen
Publisher : Springer Science & Business Media
ISBN 13 : 0817681701
Total Pages : 292 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Arithmetic of Higher-Dimensional Algebraic Varieties by : Bjorn Poonen

Download or read book Arithmetic of Higher-Dimensional Algebraic Varieties written by Bjorn Poonen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.

PROGRESS IN PHYSICS, Vol. 15. The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics

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Author : Dmitri Rabounski
Publisher : Infinite Study
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4./5 ( download)

Book Synopsis PROGRESS IN PHYSICS, Vol. 15. The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics by : Dmitri Rabounski

Download or read book PROGRESS IN PHYSICS, Vol. 15. The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics written by Dmitri Rabounski and published by Infinite Study. This book was released on with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in Physics has been created for rapid publications on advanced studies in theoretical and experimental physics, including related themes from mathematics and astronomy.

Linear Spaces and Approximation / Lineare Räume und Approximation

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Author : Butzer
Publisher : Birkhäuser
ISBN 13 : 3034871805
Total Pages : 641 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Linear Spaces and Approximation / Lineare Räume und Approximation by : Butzer

Download or read book Linear Spaces and Approximation / Lineare Räume und Approximation written by Butzer and published by Birkhäuser. This book was released on 2013-03-08 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P. L. Butzer (Aachen) and J. Korevaar (Amsterdam). Since that auspicious beginning, others of the Oberwolfach proceedings have appeared in Birkhauser's ISNM series. The present volume is the fifth * edited at Aachen in collaboration with an external institution. It once again ad dresses itself to the most recent results on approximation and operator theory, and includes 47 of the 48 lectures presented at Oberwolfach, as well as five articles subsequently submitted by V. A. Baskakov (Moscow), H. Esser (Aachen), G. Lumer (Mons), E. L. Stark (Aachen) and P. M. Tamrazov (Kiev). In addition, there is a section devoted to new and unsolved problems, based upon two special problem sessions augmented by later communications from the participants. Corresponding to the nature of the conference, the aim of the organizers was to solicit both specialized and survey papers, ranging in the broad area of classical and functional analysis, from approximation and interpolation theory to Fourier and harmonic analysis, and to the theory of function spaces and operators. The papers were supplemented by lectures on fields represented for the first time in our series of Oberwolfach Conferences, so for example, complex function theory or probability and sampling theory.

Fourier Analysis and Approximation Theory

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Author : György Alexits
Publisher :
ISBN 13 :
Total Pages : 468 pages
Book Rating : 4.:/5 (321 download)

Book Synopsis Fourier Analysis and Approximation Theory by : György Alexits

Download or read book Fourier Analysis and Approximation Theory written by György Alexits and published by . This book was released on 1976 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Harmonic and Applied Analysis

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Author : Stephan Dahlke
Publisher : Birkhäuser
ISBN 13 : 3319188631
Total Pages : 268 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis Harmonic and Applied Analysis by : Stephan Dahlke

Download or read book Harmonic and Applied Analysis written by Stephan Dahlke and published by Birkhäuser. This book was released on 2015-09-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Canadian Mathematical Bulletin

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Author :
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4./5 ( download)

Book Synopsis Canadian Mathematical Bulletin by :

Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1983-09 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: