Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$

Author: A. L. Levin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 166

ISBN-13: 0821825992

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Bounds for orthogonal polynomials which hold on the 'whole' interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on [-1,1]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Orthogonal Polynomials for Exponential Weights
Orthogonal Polynomials for Exponential Weights

Author: A. L. Levin

Publisher: Springer Science & Business Media

Published: 2001-06-29

Total Pages: 492

ISBN-13: 9780387989419

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The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century and undoubtedly will continue to grow in importance in the future. In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0 ; likewise, the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov-Bernstein and Nikolskii inequalities. The book will be of interest to researchers in approximation theory, harmonic analysis, numerical analysis, potential theory, and all those that apply orthogonal polynomials.

Orthogonal Polynomials for Exponential Weights
Orthogonal Polynomials for Exponential Weights

Author: Eli Levin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 472

ISBN-13: 1461302013

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The analysis of orthogonal polynomials associated with general weights has been a major theme in classical analysis this century. In this monograph, the authors define and discuss their classes of weights, state several of their results on Christoffel functions, Bernstein inequalities, restricted range inequalities, and record their bounds on the orthogonal polynomials, as well as their asymptotic results. This book will be of interest to researchers in approximation theory, potential theory, as well as in some branches of engineering.

Author:

Publisher: Springer Nature

Published:

Total Pages: 598

ISBN-13: 3031651332

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Finite Rational Matrix Groups
Finite Rational Matrix Groups

Author: Gabriele Nebe

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 158

ISBN-13: 0821803433

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The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and with restrictions in dimensions and p +1 and p-1 for all prime numbers p. Nonmaximal finite groups might act on several types of lattices and therefore embed into more than one maximal finite group. This gives rise to a simplicial complex interrelating the maximal finite groups and measuring the complexity of the dimension. Group theory, integral representation theory, arithmetic theory of quadratic forms and algorithmic methods are used.

Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$
Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$

Author: Mauro Beltrametti

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 79

ISBN-13: 0821802348

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This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.

Limit Theorems of Polynomial Approximation with Exponential Weights
Limit Theorems of Polynomial Approximation with Exponential Weights

Author: Michael I. Ganzburg

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 178

ISBN-13: 0821840630

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The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.

Global Aspects of Homoclinic Bifurcations of Vector Fields
Global Aspects of Homoclinic Bifurcations of Vector Fields

Author: Ale Jan Homburg

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 143

ISBN-13: 0821804413

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In this book, the author investigates a class of smooth one parameter families of vector fields on some $n$-dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families $x_\mu$, where $x_0$ has a distinguished hyperbolic singularity $p$ and a homoclinic orbit; an orbit converging to $p$ both for positive and negative time. It is assumed that this homoclinic orbit is of saddle-saddle type, characterized by the existence of well-defined directions along which it converges to the singularity $p$. The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes.

Tilting in Abelian Categories and Quasitilted Algebras
Tilting in Abelian Categories and Quasitilted Algebras

Author: Dieter Happel

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 103

ISBN-13: 0821804448

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We generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.