Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus.

This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary-value problems for differential equations of fractional order. In particular, we show the positive definiteness of studying operators, which makes it possible to select areas in the complex plane where there are no eigenvalues for these operators. [ABSTRACT FROM AUTHOR]