Harmonic Function Theory

Author : Sheldon Axler,Paul Bourdon,Ramey Wade
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 53,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475781373

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Harmonic Function Theory by Sheldon Axler,Paul Bourdon,Ramey Wade Pdf

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.

Author : Sheldon Axler,Paul Bourdon,Wade Ramey
Publisher : Springer
Page : 238 pages
File Size : 48,6 Mb
Release : 2006-05-04
Category : Mathematics
ISBN : 9780387215273

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Harmonic Function Theory by Sheldon Axler,Paul Bourdon,Wade Ramey Pdf

Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.

Author : Sheldon Axler,Paul Bourdon,Ramey Wade
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 40,8 Mb
Release : 2001-01-25
Category : Mathematics
ISBN : 9780387952185

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Harmonic Function Theory by Sheldon Axler,Paul Bourdon,Ramey Wade Pdf

This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.

Author : Anonim
Publisher : Unknown
Page : 231 pages
File Size : 49,5 Mb
Release : 1992
Category : Harmonic functions
ISBN : 1489911863

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Harmonic Function Theory by Anonim Pdf

Author : Daniel Harrison
Publisher : University of Chicago Press
Page : 364 pages
File Size : 40,9 Mb
Release : 1994-05-28
Category : Music
ISBN : 0226318087

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Harmonic Function in Chromatic Music by Daniel Harrison Pdf

Applicable on a wide scale not only to this repertory, Harrison's lucid explications of abstract theoretical concepts provide new insights into the workings of tonal systems in general.

Author : Ross G. Pinsky
Publisher : Cambridge University Press
Page : 492 pages
File Size : 52,7 Mb
Release : 1995-01-12
Category : Mathematics
ISBN : 9780521470148

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Positive Harmonic Functions and Diffusion by Ross G. Pinsky Pdf

In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.

Author : R.E. Greene,H. Wu
Publisher : Springer
Page : 219 pages
File Size : 49,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540355366

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Function Theory on Manifolds Which Possess a Pole by R.E. Greene,H. Wu Pdf

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 44,8 Mb
Release : 2009-05-24
Category : Mathematics
ISBN : 9780817646691

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Explorations in Harmonic Analysis by Steven G. Krantz Pdf

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 : Victor Anandam
Publisher : Springer Science & Business Media
Page : 152 pages
File Size : 52,8 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9783642213991

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Harmonic Functions and Potentials on Finite or Infinite Networks by Victor Anandam Pdf

Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.

Author : Cho-Ho Chu,Anthony To-Ming Lau
Publisher : Springer
Page : 100 pages
File Size : 53,7 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540477938

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Harmonic Functions on Groups and Fourier Algebras by Cho-Ho Chu,Anthony To-Ming Lau Pdf

This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.

Author : Carlos A. Berenstein,Roger Gay
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384458

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Complex Analysis and Special Topics in Harmonic Analysis by Carlos A. Berenstein,Roger Gay Pdf

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 : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 52,9 Mb
Release : 2001
Category : Functions of several complex variables
ISBN : 9780821827246

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Function Theory of Several Complex Variables by Steven George Krantz Pdf

Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Author : Rodrigo Banuelos,Charles N. Moore
Publisher : Birkhäuser
Page : 220 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887281

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Probabilistic Behavior of Harmonic Functions by Rodrigo Banuelos,Charles N. Moore Pdf

Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This monograph, aimed at researchers and students in these fields, explores several aspects of this relationship. The primary focus of the text is the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. The text first gives the requisite background material from harmonic analysis and discusses known results concerning the nontangential maximal function and area function, as well as the central and essential role these have played in the development of the field.The book next discusses further refinements of traditional results: among these are sharp good-lambda inequalities and laws of the iterated logarithm involving nontangential maximal functions and area functions. Many applications of these results are given. Throughout, the constant interplay between probability and harmonic analysis is emphasized and explained. The text contains some new and many recent results combined in a coherent presentation.

Author : Corneliu Constantinescu,Aurel Cornea
Publisher : Springer
Page : 0 pages
File Size : 48,9 Mb
Release : 2012-01-16
Category : Mathematics
ISBN : 3642654347

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Potential Theory on Harmonic Spaces by Corneliu Constantinescu,Aurel Cornea Pdf

There has been a considerable revival of interest in potential theory during the last 20 years. This is made evident by the appearance of new mathematical disciplines in that period which now-a-days are considered as parts of potential theory. Examples of such disciplines are: the theory of Choquet capacities, of Dirichlet spaces, of martingales and Markov processes, of integral representation in convex compact sets as well as the theory of harmonic spaces. All these theories have roots in classical potential theory. The theory of harmonic spaces, sometimes also called axiomatic theory of harmonic functions, plays a particular role among the above mentioned theories. On the one hand, this theory has particularly close connections with classical potential theory. Its main notion is that of a harmonic function and its main aim is the generalization and unification of classical results and methods for application to an extended class of elliptic and parabolic second order partial differential equations. On the other hand, the theory of harmonic spaces is closely related to the theory of Markov processes. In fact, all important notions and results of the theory have a probabilistic interpretation.

Author : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 41,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662097564

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Representation Theory and Noncommutative Harmonic Analysis II by A.A. Kirillov Pdf

Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.