A generalization of parabolic Riesz and parabolic Bessel potentials
| Autor: | Ilham A. Aliev, Cagla Sekin |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
integral operators Generalization General Mathematics 010102 general mathematics Type (model theory) Differential operator 01 natural sciences 010101 applied mathematics symbols.namesake Identity (mathematics) 47G40 Operator (computer programming) Gauss–Weierstrass kernel parabolic potentials symbols 0101 mathematics 26A33 Laplace operator Bessel function 47G10 47B38 Mathematics |
| Zdroj: | Rocky Mountain J. Math. 50, no. 3 (2020), 815-824 |
| ISSN: | 0035-7596 |
| DOI: | 10.1216/rmj.2020.50.815 |
| Popis: | Classical parabolic Riesz and parabolic Bessel type potentials are interpreted as negative fractional powers of the differential operators (−△+∂∕∂t) and (I−△+∂∕∂t). Here, △ is the Laplacian and I is the identity operator. We introduce some generalizations of these potentials, namely, we define the family of operators Aβ,𝜃α=(𝜃I+(−△)β∕2+∂∕∂t)−α for 𝜃≥0 and α,β>0, and investigate its behavior in the framework of Lp(ℝn+1)-spaces. |
| Databáze: | OpenAIRE |
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