Inequalities for formal power series and entire functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:338

Article

Grinshpan, Arcadii Z.

关键词: integral inequalities;    convolutions;    Hadamard product;    formal power series;    entire functions of exponential type;    Borel-associated functions;    integral operators;    confluent hypergeometric functions;    Bessel functions;    Laguerre polynomials;    exponential inequalities;    trigonometric inequalities;   

DOI  :  10.1016/j.jmaa.2007.06.038

来源: Elsevier

【 摘 要 】

We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free