Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform

In an earlier paper (A. N. Kochubei, Pacif. J. Math. 269 (2014), 355–369), the author considered a restriction of Vladimirov’s fractional differentiation operator D α , α > 0 , to radial functions on a non-Archimedean field. In particular, it was found to possess such a right inverse I α that the...

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Bibliographic Details
Published in:Integral equations and operator theory 2020-12, Vol.92 (6), Article 44
Main Author: Kochubei, Anatoly N.
Format: Article
Language:English
Subjects:
Analysis
Calculus
Differential equations
Laplace transforms
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary differential equations
Volterra integral equations
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Summary:In an earlier paper (A. N. Kochubei, Pacif. J. Math. 269 (2014), 355–369), the author considered a restriction of Vladimirov’s fractional differentiation operator D α , α > 0 , to radial functions on a non-Archimedean field. In particular, it was found to possess such a right inverse I α that the appropriate change of variables reduces equations with D α (for radial functions) to integral equations whose properties resemble those of classical Volterra equations. In other words, we found, in the framework of non-Archimedean pseudo-differential operators, a counterpart of ordinary differential equations. In the present paper, we begin an operator-theoretic investigation of the operator I α , and study a related analog of the Laplace transform.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-020-02604-6