Weighted Approximation with Varying Weight
Weighted Approximation with Varying Weight

Author: Vilmos Totik

Publisher: Springer

Published: 2006-11-15

Total Pages: 119

ISBN-13: 3540483233

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A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights
Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

Author: Eli Levin

Publisher: Springer

Published: 2018-02-13

Total Pages: 168

ISBN-13: 3319729470

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This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices.

Introduction To The Theory Of Weighted Polynomial Approximation
Introduction To The Theory Of Weighted Polynomial Approximation

Author: H N Mhaskar

Publisher: World Scientific

Published: 1997-01-04

Total Pages: 398

ISBN-13: 9814518050

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In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.

Author:

Publisher: Springer Nature

Published:

Total Pages: 598

ISBN-13: 3031651332

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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.

On Artin's Conjecture for Odd 2-dimensional Representations
On Artin's Conjecture for Odd 2-dimensional Representations

Author: Gerhard Frey

Publisher: Springer

Published: 2006-11-15

Total Pages: 160

ISBN-13: 354048681X

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The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols. It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.

Phase Transitions and Hysteresis
Phase Transitions and Hysteresis

Author: Augusto Visintin

Publisher: Springer

Published: 2006-11-15

Total Pages: 301

ISBN-13: 354048678X

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1) Phase Transitions, represented by generalizations of the classical Stefan problem. This is studied by Kenmochi and Rodrigues by means of variational techniques. 2) Hysteresis Phenomena. Some alloys exhibit shape memory effects, corresponding to a stress-strain relation which strongly depends on temperature; mathematical physical aspects are treated in Müller's paper. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions; their properties are studied by Brokate. 3) Numerical analysis. Several models of the phenomena above can be formulated in terms of nonlinear parabolic equations. Here Verdi deals with the most updated approximation techniques.

Finsler Metrics - A Global Approach
Finsler Metrics - A Global Approach

Author: Marco Abate

Publisher: Springer

Published: 2006-11-15

Total Pages: 185

ISBN-13: 354048812X

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Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.

Difference Spaces and Invariant Linear Forms
Difference Spaces and Invariant Linear Forms

Author: Rodney Nillsen

Publisher: Springer

Published: 2006-11-15

Total Pages: 198

ISBN-13: 3540486526

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Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, e.g., the origin. One aim is to establish connections between these spaces and differential operators, singular integral operators and wavelets. Another aim is to discuss aspects of these ideas which emphasise invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a clear, accessible and unified viewpoint, which emphasises connections with related work.

Gorenstein Dimensions
Gorenstein Dimensions

Author: Lars W. Christensen

Publisher: Springer Science & Business Media

Published: 2000-11-06

Total Pages: 220

ISBN-13: 9783540411321

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This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content. Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.