Generalized Bessel potential and its application to non-homogeneous singular screened Poisson equation


Shishkina E., Ekincioglu İ., Keskin C.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol.32, no.12, pp.932-947, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Review
  • Volume: 32 Issue: 12
  • Publication Date: 2021
  • Doi Number: 10.1080/10652469.2020.1867983
  • Journal Name: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.932-947
  • Keywords: Bessel operator, generalized Bessel potential, singular screened Poisson equation, generalized Bochner formula

Abstract

In this paper, generalized Bessel potential is studied. A generalization is achieved by considering the singular Laplace-Bessel operator instead of the Laplace operator in the construction of the Bessel potential. First, we give some auxiliary statements as weighted plane wave relation and generalized Bochner formula. Next, we consider the Bessel kernel and prove some of its properties. After that, we present the definition and properties of generalized Bessel potential. Finally, we consider the generalized Bessel potential as a solution to the singular screened Poisson equation.