The Analytic Continuation of the Riemannliouville Integral in the Hyperbolic Case

Autor:	Marcel Riesz
Rok vydání:	1961
Předmět:	symbols.namesake General Mathematics Analytic continuation Riemann–Liouville integral Mathematical analysis Global analytic function Hyperbolic function symbols Inverse hyperbolic function Mathematics
Zdroj:	Canadian Journal of Mathematics. 13:37-47
ISSN:	1496-4279 0008-414X
DOI:	10.4153/cjm-1961-003-x
Popis:	In 1949 I published in the Acta Mathematica (vol. 81) a rather long paper: “L'intégrale de Riemann-Liouville et le problème de Cauchy.” This work will be quoted in the sequel as Acta paper. Only minor local references to this paper will be made here, and knowledge of it is not required for the reading of the present article. The notations used here are slightly different from those used in my former paper.In the Acta paper I introduce multiple integrals and of the Riemann- Liouville type depending on a parameter α and converging for sufficiently large values of α. I give the solution of the Cauchy problem for the wave equation in a unique formula, the same for space-time of odd or even dimensions, implying an analytic continuation with respect to the parameter α.
Databáze:	OpenAIRE
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