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505 pages

Logarithmic Potentials with External Fields

Creator: Edward B. Saff, Vilmos Totik | Mathematics - 1997-10-09

This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the ...

Publisher: Springer Science & Business Media

About this book
In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of approximation theoretical techniques with classical potential theory (more precisely, the theory of logarithmic potentials, which is directly related to polynomials and to problems in the plane or on the real line). Most of the applications are based on an exten sion of classical logarithmic potential theory to the case when there is a weight (external field) present. The list of recent developments is quite impressive and includes: creation of the theory of non-classical orthogonal polynomials with re spect to exponential weights; the theory of orthogonal polynomials with respect to general measures with compact support; the theory of incomplete polynomials and their widespread generalizations, and the theory of multipoint Pade approximation. The new approach has produced long sought solutions for many problems; most notably, the Freud problems on the asymptotics of orthogonal polynomials with a respect to weights of the form exp(-Ixl ); the "l/9-th" conjecture on rational approximation of exp(x); and the problem of the exact asymptotic constant in the rational approximation of Ixl. One aim of the present book is to provide a self-contained introduction to the aforementioned "weighted" potential theory as well as to its numerous applications. As a side-product we shall also fully develop the classical theory of logarithmic potentials.



357 pages

A History of Japan, 1582-1941, Internal and External Worlds

Creator: L. M. Cullen | Business & Economics - 2003-05-15

Distinctive overview of the internal and external pressures responsible for the emergence of modern Japan.

Publisher: Cambridge University Press

About this book
This 2003 book offers a distinctive overview of the internal and external pressures responsible for the emergence of modern Japan.



266 pages

Our Knowledge of the External World

Creator: Bertrand Russell | Knowledge, Theory of - 1914

Publisher: New York, Norton


1000 GB and Up Directory

External | Definition of External by Merriam-Webster
Define external: located, seen, or used on the outside or surface of something — external in a sentence

External - definition of external by The Free Dictionary
In Tom's external situation, at this time, there was, as the world says, nothing to complain of Little Eva's fancy for him--the instinctive gratitude and loveliness ...

External | Define External at Dictionary.com
External definition, of or relating to the outside or outer part; outer: an external surface. See more.

External Synonyms, External Antonyms | Thesaurus.com
Synonyms for external at Thesaurus.com with free online thesaurus, antonyms, and definitions. Dictionary and Word of the Day.

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1000 GB and Up


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