Stieltjes differential-boundary operators. III. Multivalued operators–linear relations

Allan Morton Krall

Vol. 59 (1975), No. 1, 125–134

DOI: 10.2140/pjm.1975.59.125

Abstract

This article deals with a multivalued differential-boundary operator on a nondense domain regarding it as a linear relation. The adjoint relation is derived. It is shown that these dual relations have the same form as exhibited in earlier papers where the operators involved were uniquely defined on dense domains. Self-adjoint relations are considered on the Hilbert space ℒ_n²[0,1]. The connection with self-adjoint operators defined on subspaces of ℒ_n²[0,1] is made.

Mathematical Subject Classification 2000

Primary: 47A50

Secondary: 34B25

Milestones

Received: 16 October 1974

Revised: 25 March 1975

Published: 1 July 1975