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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Logarithmic Potentials with External Fields (Paperback, Softcover reprint of hardcover 1st ed. 1997)
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Logarithmic Potentials with External Fields (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Series: Grundlehren der mathematischen Wissenschaften, 316
Expected to ship within 10 - 15 working days
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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."
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