Interpolation And Approximation By Rational Functions In The Complex Domains
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Interpolation And Approximation By Rational Functions In The Complex Domain
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Author : J. L. Walsh
language : en
Publisher: American Mathematical Soc.
Release Date : 1935-12-31
Interpolation And Approximation By Rational Functions In The Complex Domain written by J. L. Walsh and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1935-12-31 with Mathematics categories.
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.
Interpolation And Approximation By Rational Functions In The Complex Domains
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Author : J.L. Walsh
language : en
Publisher:
Release Date : 1956
Interpolation And Approximation By Rational Functions In The Complex Domains written by J.L. Walsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with categories.
Interpolation By Harmonic Polynomials
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Author : John Hamilton Curtiss
language : en
Publisher:
Release Date : 1961
Interpolation By Harmonic Polynomials written by John Hamilton Curtiss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Interpolation categories.
Let Hn (u;z) denote the harmonic polynomial of degree at most n found by interpolation in 2n +1 points in a function u given on the boundary C of a region D of the complex z-plane. Explict formulas are derived for Hn in the case of interpolation on a circle and on an ellipse, and convergence is proved in these cases for arbitrary continuous boundary data. Various generalizations are indicated.
Interpolation And Approximation By Rational Functions In The Complex Domain
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Author : J. L. Walsh
language : en
Publisher: American Mathematical Soc.
Release Date : 1965
Interpolation And Approximation By Rational Functions In The Complex Domain written by J. L. Walsh and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.
The Analysis Of Solutions Of Elliptic Equations
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Author : Nikolai Tarkhanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Analysis Of Solutions Of Elliptic Equations written by Nikolai Tarkhanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L- rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on ill-posedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts.
Global Solutions Of Nonlinear Schrodinger Equations
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Author : Jean Bourgain
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Global Solutions Of Nonlinear Schrodinger Equations written by Jean Bourgain and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.
Canadian Mathematical Bulletin
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Author :
language : en
Publisher:
Release Date : 1995-06
Canadian Mathematical Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06 with categories.
Chiral Algebras
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Author : Alexander Beilinson
language : en
Publisher: American Mathematical Society
Release Date : 2025-06-17
Chiral Algebras written by Alexander Beilinson and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-17 with Mathematics categories.
Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras. The exposition of this book covers the following topics: the “classical” counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries; the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the chiral algebras of differential operators; the formalism of chiral homology treating “the space of conformal blocks” of the conformal field theory, which is a “quantum” counterpart of the space of the global solutions of a differential equation. The book will be of interest to researchers working in algebraic geometry and its applications to mathematical physics and representation theory.
The Calculus Of Variations In The Large
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Author : Marston Morse
language : en
Publisher: American Mathematical Soc.
Release Date : 1934-12-31
The Calculus Of Variations In The Large written by Marston Morse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934-12-31 with Mathematics categories.
Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.
The Book Of Involutions
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Author : Max-Albert Knus
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
The Book Of Involutions written by Max-Albert Knus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.