Boundary Criterion for Integral Operators

T. Sh. Kal’menov and M. Otelbaev

Presented by Academician E.I. Moiseev July 15, 2015

Received August 21, 2015

Abstract—Integral operators of the form f(x) = (x, t)f(t)dt for the case of a finite domain Rⁿ with
smooth boundary are considered. Conditions on the real kernel K(x, t) of an integral operator under which
this operator satisfies a well-defined boundary condition for the corresponding differential equation are found.
The application of the results is demonstrated on the example of a Sturm–Liouville equation, for which the der-
ivation of the general form of well-posed boundary value problems is presented.

DOI: 10.1134/S1064562416010208

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