Singular integrals and positive kernels

Calvin R. Putnam

Vol. 27 (1968), No. 2, 379–386

DOI: 10.2140/pjm.1968.27.379

Abstract

Let k(x,t) be a C¹ kernel of a positive integral operator on L²(E) where E is compact. It is shown that certain singular self-adjoint operators A on L²(E), consisting of the sum of a multiplication operator and a generalized Hilbert transform integral operator with Kernel ik(x,t)(x − t)⁻¹, are analogous to—sometimes even to the extent of unitary equivalence—operators, about which a good deal more is known, of the same structure as A but with k(x,t) of the special form ϕ(x)ϕ(t).

Mathematical Subject Classification

Primary: 47.70

Milestones

Received: 22 June 1967

Published: 1 November 1968