On a generalized function-to-sequence transform

Applicable Analysis and Discrete Mathematics

article

Slobodan B. Tričković¹  Miomir Stanković² 

[1] Department of Mathematics, Faculty of Civil Engineering, University of Niˇs;Mathematical Institute of the Serbian Academy of Sciences and Arts

关键词: Binomial transform;    forward difference operator;    generalized function-to-sequence transform;    Bessel's operator;   

DOI  :  10.2298/AADM180908005T

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

By attaching a sequence {αn}n∈N0to the binomial transform, a new operator Dα is obtained. We use the same sequence to define a new transformTα mapping derivatives to the powers of Dα, and integrals to D−1α . The inverse transform Bα of Tα is introduced and its properties are studied. Forαn = (−1)n, Bα reduces to the Borel transform. Applying Tα to Bessel’sdifferential operator ddx xddx , we obtain Bessel’s discrete operator DαnNα. Itseigenvectors correspond to eigenfunctions of Bessel’s differential operator.

【 授权许可】

Unknown