Absolutely continuous component of a class of integral operators

Sours, Richard E.

doi:10.1090/S0002-9939-1973-0312333-1

Absolutely continuous component of a class of integral operators
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by Richard E. Sours PDF

Proc. Amer. Math. Soc. 37 (1973), 521-524 Request permission

Abstract:

The operator $T:{L^2}(0,\infty ) \to {L^2}(0,\infty )$ defined by \[ Tf(x) = \int _0^\infty {\frac {{k(x){{(k(t))}^ - }}}{{x + t}}} \;f(t)\;dt,\] where ${(k(t))^ - }$ is the complex conjugate, is studied and conditions are given which are sufficient to characterize the absolutely continuous component.

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