Open Access

# Automorphisms generated by umbral calculus on a nuclear space of entire test functions

### Abstract

In this paper we show that Sheffer operators, mapping monomials to certain Sheffer polynomial sequences, such as falling and rising factorials, Charlier, and Hermite polynomials extend to continuous automorphisms on the space of entire functions of first order growth and minimal type.

Key words: White noise theory, umbral calculus, topological spaces of test functions, special classes of entire functions and growth estimates.

### Article Information

 Title Automorphisms generated by umbral calculus on a nuclear space of entire test functions Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 4, 339-348 MathSciNet MR3912069 Milestones Received 05/09/2017; Revised 24/05/2018 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

Ferdinand Jamil
Department of Mathematics and Statistics, MSU-Iligan Institute of technology, Iligan City, Philippines

Yuri Kondratiev
Faculty of Mathematics, Bielefeld University, Germany

Sheila Menchavez
Department of Mathematics and Statistics, MSU-Iligan Institute of technology, Iligan City, Philippines

Ludwig Streit
BiBoS, Bielefeld University, Germany; CCM, Universidade da Madeira, Funchal, Portugal

### Citation Example

Ferdinand Jamil, Yuri Kondratiev, Sheila Menchavez, and Ludwig Streit, Automorphisms generated by umbral calculus on a nuclear space of entire test functions, Methods Funct. Anal. Topology 24 (2018), no. 4, 339-348.

### BibTex

@article {MFAT1112,
AUTHOR = {Ferdinand Jamil and Yuri Kondratiev and Sheila Menchavez and Ludwig Streit},
TITLE = {Automorphisms generated by umbral calculus on a nuclear space of entire test functions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {4},
PAGES = {339-348},
ISSN = {1029-3531},
MRNUMBER = {MR3912069},
URL = {http://mfat.imath.kiev.ua/article/?id=1112},
}

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