Vol. 27, No. 2, 1968

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ISSN: 0030-8730
Singular integrals and positive kernels

Calvin R. Putnam

Vol. 27 (1968), No. 2, 379–386

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
Received: 22 June 1967
Published: 1 November 1968
Calvin R. Putnam