This article is cited in 8 papers

The Legendre operator function

A. V. Glushak

Voronezh State Technical University

Abstract: We study the properties of the resolving operator of the Cauchy problem for an abstract Legendre equation with an unbounded linear operator $A$. We establish a relationship between this resolving operator and that of the Cauchy problem for an abstract Euler–Poisson–Darboux equation and prove the coincidence of the sets of operators $A$ for which the Cauchy problems for the Legendre and Euler–Poisson–Darboux equations are uniformly well posed.

MSC: 34G10, 35Q05, 35K99, 35L15, 43A90, 47D06, 53B21, 53C65

Received: 20.03.1998

DOI: 10.4213/im363

 English version: Izvestiya: Mathematics, 2001, 65:6, 1073–1083

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