Vol. 81, No. 2, 1979

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ISSN: 0030-8730
Eigenfunction expansions for selfadjoint integro-differential operators

Robert Charles Carlson

Vol. 81 (1979), No. 2, 327–347
Abstract

Let be a self-adjoint ordinary differential operator on a Hilbert space L2(), an open interval, while 𝒦 will denote a bounded self-adjoint operator on the same space. An eigenfunction expansion associated with H = + 𝒦 is developed when 𝒦 is an integral operator whose kernel K(x,y) has compact support in ℐ×ℐ. It is assumed that if f = k=0nak(x)Dkf, where D = (d∕dx), then ak Ck(), k = 0,,n, and an(x)0 for x ∈ℐ.

Mathematical Subject Classification 2000
Primary: 47G05, 47G05
Secondary: 45J05
Milestones
Received: 21 January 1978
Published: 1 April 1979
Authors
Robert Charles Carlson