This article is cited in 14 papers

Extensions of Laguerre operators in indefinite inner product spaces

V. A. Derkach

Donetsk National University

Abstract: The Laguerre–Sonin polynomials $L_n^{(\alpha)}$ are orthogonal in linear spaces with indefinite inner product if $\alpha<-1$. We construct the completion $\Pi(\alpha)$ of this space and describe self-adjoint extensions of the Laguerre operator $l(y)=xy''+(1+\alpha-x)y'$, $\alpha<-1$, in the space $\Pi(\alpha)$. In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre–Sonin polynomials and form an orthogonal basis in $\Pi(\alpha)$.

UDC: 517.98

Received: 13.05.1996
Revised: 23.10.1997

DOI: 10.4213/mzm1311

 English version: Mathematical Notes, 1998, 63:4, 449–459

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