Wiman–Valiron theory for a polynomial series based on the Wilson operator

Kam Hang Cheng

doi:10.1016/j.jat.2018.12.002

Wiman–Valiron theory for a polynomial series based on the Wilson operator

Kam Hang Cheng

Department of Mathematics

Research output: Contribution to journal › Journal Article › peer-review

4 Citations (Scopus)

Abstract

We establish a Wiman–Valiron theory for a polynomial series based on the Wilson operator D_W. For an entire function f of order smaller than [Formula presented], this theory includes (i) an estimate which shows that f behaves locally like a polynomial consisting of the terms near the maximal term in its Wilson series expansion, and (ii) an estimate of D_W ⁿf compared to f. We then apply this theory in studying the growth of entire solutions to difference equations involving the Wilson operator.

Original language	English
Pages (from-to)	174-209
Number of pages	36
Journal	Journal of Approximation Theory
Volume	239
DOIs	https://doi.org/10.1016/j.jat.2018.12.002
Publication status	Published - Mar 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Complex difference equations
Complex function theory
Interpolation series
Wilson operator
Wiman–Valiron theory

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10.1016/j.jat.2018.12.002

Cite this

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abstract = "We establish a Wiman–Valiron theory for a polynomial series based on the Wilson operator DW. For an entire function f of order smaller than [Formula presented], this theory includes (i) an estimate which shows that f behaves locally like a polynomial consisting of the terms near the maximal term in its Wilson series expansion, and (ii) an estimate of DW nf compared to f. We then apply this theory in studying the growth of entire solutions to difference equations involving the Wilson operator.",

keywords = "Complex difference equations, Complex function theory, Interpolation series, Wilson operator, Wiman–Valiron theory",

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year = "2019",

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doi = "10.1016/j.jat.2018.12.002",

language = "English",

volume = "239",

pages = "174--209",

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AU - Cheng, Kam Hang

PY - 2019/3

Y1 - 2019/3

N2 - We establish a Wiman–Valiron theory for a polynomial series based on the Wilson operator DW. For an entire function f of order smaller than [Formula presented], this theory includes (i) an estimate which shows that f behaves locally like a polynomial consisting of the terms near the maximal term in its Wilson series expansion, and (ii) an estimate of DW nf compared to f. We then apply this theory in studying the growth of entire solutions to difference equations involving the Wilson operator.

AB - We establish a Wiman–Valiron theory for a polynomial series based on the Wilson operator DW. For an entire function f of order smaller than [Formula presented], this theory includes (i) an estimate which shows that f behaves locally like a polynomial consisting of the terms near the maximal term in its Wilson series expansion, and (ii) an estimate of DW nf compared to f. We then apply this theory in studying the growth of entire solutions to difference equations involving the Wilson operator.

KW - Complex difference equations

KW - Complex function theory

KW - Interpolation series

KW - Wilson operator

KW - Wiman–Valiron theory

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000459368700008

UR - https://openalex.org/W2796961561

UR - https://www.scopus.com/pages/publications/85059184195

U2 - 10.1016/j.jat.2018.12.002

DO - 10.1016/j.jat.2018.12.002

M3 - Journal Article

SN - 0021-9045

VL - 239

SP - 174

EP - 209

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

Wiman–Valiron theory for a polynomial series based on the Wilson operator

Abstract

Bibliographical note

Keywords

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