Explorations in Harmonic Analysis PDF Download
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Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646698
Category : Mathematics
Languages : en
Pages : 367
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Book Description
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.
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646698
Category : Mathematics
Languages : en
Pages : 367
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Book Description
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.
Author: Carlos A. Berenstein
Publisher: Springer Science & Business Media
ISBN: 1461384451
Category : Mathematics
Languages : en
Pages : 491
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Book Description
A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.
Author: Nakhlé H. Asmar
Publisher: Springer
ISBN: 3319940635
Category : Mathematics
Languages : en
Pages : 501
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Book Description
This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences. The overall aim in designing this text is to accommodate students of different mathematical backgrounds and to achieve a balance between presentations of rigorous mathematical proofs and applications. The text is adapted to enable maximum flexibility to instructors and to students who may also choose to progress through the material outside of coursework. Detailed examples may be covered in one course, giving the instructor the option to choose those that are best suited for discussion. Examples showcase a variety of problems with completely worked out solutions, assisting students in working through the exercises. The numerous exercises vary in difficulty from simple applications of formulas to more advanced project-type problems. Detailed hints accompany the more challenging problems. Multi-part exercises may be assigned to individual students, to groups as projects, or serve as further illustrations for the instructor. Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results. Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website. Additional solutions for instructors’ use may be obtained by contacting the authors directly.
Author: Tarlok Nath Shorey
Publisher: Springer Nature
ISBN: 9811590974
Category : Mathematics
Languages : en
Pages : 287
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Book Description
The book discusses major topics in complex analysis with applications to number theory. This book is intended as a text for graduate students of mathematics and undergraduate students of engineering, as well as to researchers in complex analysis and number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory. In additional to solved examples and problems, the book covers most of the topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, gamma function and harmonic functions.
Author: Robert Deville
Publisher: CRC Press
ISBN: 9780582286986
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Multivariable complex analysis and harmonic analysis provide efficient techniques to study many applied mathematical problems. The main objective of a conference held in Bordeaux in June 1995, in honour of Professor Roger Gay, was to connect these mathematical fields with some of their applications. This was also the guideline for the fourteen contributions collected in this volume. Besides presenting new results, each speaker made a substantial effort in order to present an up to date survey of his field of research. All the subjects presented here are very active domains of research: integral geometry (with its relation to X-ray tomography), classical harmonic analysis and orthogonal polynomials, pluricomplex potential theory (with its deep connection with polynomial approximation), complex analytic methods in the theory of partial differentiable operators with constant coefficients (in the spirit of those initiated by Leon Ehrenpreis), Calderon-Zygmund operators and nonlinear operators, oscillatory integrals and resonance, and finally multivariable residue theory in its most recent developments. It is hoped that the reader will find enough insight in the different survey papers presented here to become involved with one of these subjects or to pursue further applications.
Author: Mkhitar M. Djrbashian
Publisher: Springer Science & Business Media
ISBN: 9783764328559
Category : Mathematics
Languages : en
Pages : 280
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Book Description
1 Preliminary results. Integral transforms in the complex domain.- 1.1 Introduction.- 1.2 Some identities.- 1.3 Integral representations and asymptotic formulas.- 1.4 Distribution of zeros.- 1.5 Identities between some Mellin transforms.- 1.6 Fourier type transforms with Mittag-Leffler kernels.- 1.7 Some consequences.- 1.8 Notes.- 2 Further results. Wiener-Paley type theorems.- 2.1 Introduction.- 2.2 Some simple generalizations of the first fundamental Wiener-Paley theorem.- 2.3 A general Wiener-Paley type theorem and some particular results.- 2.4 Two important cases of the general Wiener-Paley type theorem.- 2.5 Generalizations of the second fundamental Wiener-Paley theorem.- 2.6 Notes.- 3 Some estimates in Banach spaces of analytic functions.- 3.1 Introduction.- 3.2 Some estimates in Hardy classes over a half-plane.- 3.3 Some estimates in weighted Hardy classes over a half-plane.- 3.4 Some estimates in Banach spaces of entire functions of exponential type.- 3.5 Notes.- 4 Interpolation series expansions in spacesW1/2, ?p, ?of entire functions.- 4.1 Introduction.- 4.2 Lemmas on special Mittag-Leffler type functions.- 4.3 Two special interpolation series.- 4.4 Interpolation series expansions.- 4.5 Notes.- 5 Fourier type basic systems inL2(0, ?).- 5.1 Introduction.- 5.2 Biorthogonal systems of Mittag-Leffler type functions and their completeness inL2(0, ?).- 5.3 Fourier series type biorthogonal expansions inL2(0, ?).- 5.4 Notes.- 6 Interpolation series expansions in spacesWs+1/2, ?p, ?of entire functions.- 6.1 Introduction.- 6.2 The formulation of the main theorems.- 6.3 Auxiliary relations and lemmas.- 6.4 Further auxiliary results.- 6.5 Proofs of the main theorems.- 6.6 Notes.- 7 Basic Fourier type systems inL2spaces of odd-dimensional vector functions.- 7.1 Introduction.- 7.2 Some identities.- 7.3 Biorthogonal systems of odd-dimensional vector functions.- 7.4 Theorems on completeness and basis property.- 7.5 Notes.- 8 Interpolation series expansions in spacesWs, ?p, ?of entire functions.- 8.1 Introduction.- 8.2 The formulation of the main interpolation theorem.- 8.3 Auxiliary relations and lemmas.- 8.4 Further auxiliary results.- 8.5 The proof of the main interpolation theorem.- 8.6 Notes.- 9 Basic Fourier type systems inL2spaces of even-dimensional vector functions.- 9.1 Introduction.- 9.2 Some identities.- 9.3 The construction of biorthogonal systems of even-dimensional vector functions.- 9.4 Theorems on completeness and basis property.- 9.5 Notes.- 10 The simplest Cauchy type problems and the boundary value problems connected with them.- 10.1 Introduction.- 10.2 Riemann-Liouville fractional integrals and derivatives.- 10.3 A Cauchy type problem.- 10.4 The associated Cauchy type problem and the analog of Lagrange formula.- 10.5 Boundary value problems and eigenfunction expansions.- 10.6 Notes.- 11 Cauchy type problems and boundary value problems in the complex domain (the case of odd segments).- 11.1 Introduction.- 11.2 Preliminaries.- 11.3 Cauchy type problems and boundary value problems containing the operators $$ {\mathbb{L}_{s + 1/2}}$$ and $$ \mathbb{L}_{s + 1/2} *$$.- 11.4 Expansions inL2{?2s+1(?)} in terms of Riesz bases.- 11.5 Notes.- 12 Cauchy type problems and boundary value problems in the complex domain (the case of even segments).- 12.1 Introduction.- 12.2 Preliminaries.- 12.3 Cauchy type problems and boundary value problems containing the operators $${{\mathbb{L}}_{s}} $$ and $$ \mathbb{L}_{s} *$$.- 12.4 Expansions inL2{?2s(?)} in terms of Riesz bases.- 12.5
Author: Camil Muscalu
Publisher: Cambridge University Press
ISBN: 1107031826
Category : Mathematics
Languages : en
Pages : 341
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Book Description
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Author: Luogeng Hua
Publisher: American Mathematical Soc.
ISBN: 0821815563
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Author: Mladen Victor Wickerhauser
Publisher: Springer Science & Business Media
ISBN: 0817648801
Category : Mathematics
Languages : en
Pages : 317
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Book Description
This textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebra and analysis, the work examines tools used to create application software for multimedia signal processing and communication. Replete with exercises, sample programs in Standard C, and numerous illustrations, Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to contemporary mathematics with practical applications. The work may also serve as an invaluable reference for multimedia applications developers and all those interested in the mathematics underlying multimedia design and implementation.
Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 9780486647623
Category : Mathematics
Languages : en
Pages : 308
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Book Description
The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.
