Unified Approach to Uniqueness, Expansion and Approximation Problems

By: Chiu-cheng Chang

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Hardcover | 1 December 1993

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120 Pages

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22.86 x 16.51 x 1.91

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This text introduces the concept of Polya property for holomorphic functions of two and several variables. The functions which have the Polya property are used to study the uniqueness problem for entire functions. This gives interesting results for a general class of generating functions. The functions with Polya property are used as generating kernels in formal generating relations to study the expansion problem for entire functions. A necessary and sufficient condition is obtained for an entire function to have a unique expansion in a series of various known polynomials generated from the formal generating relations. In this book it is shown that the uniqueness problem for entire functions of exponential type is equivalent to the approximation problem for analytic functions. Since functions with Polya property have very useful applications, the study of a class of linear operators which preserve the Polya property is embarked upon and two sufficient conditions for an operator to be Polya-property-preserving are given.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Calculus & Mathematical Analysis Functional Analysis & Transforms Calculus of Variations Differential Calculus & Equations Booktopia Publisher Services World Scientific Publishing

Background	p. 1
Introduction	p. 13
The Polya Property	p. 20
The Polya Property and Uniqueness	p. 33
The Polya Property and Expansion	p. 47
The Polya Property and Approximation	p. 68
A Class of Polya Property Preserving Operators	p. 80
Bibliography	p. 103
Index	p. 107
Table of Contents provided by Blackwell. All Rights Reserved.

Unified Approach to Uniqueness, Expansion and Approximation Problems

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Hardcover

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