Operators Whose Resolvents Have Convolution Representations and their Spectral Analysis
Kanguzhin B.E.
January 2021Springer
Journal of Mathematical Sciences (United States)
2021#252Issue 3384 - 398 pp.
In this paper, we study spectral decompositions with respect to a system of generalized eigenvectors of second-order differential operators on an interval whose resolvents possess convolution representations. We obtain the convolution representation of resolvents of second-order differential operators on an interval with integral boundary conditions. Then, using the convolution generated by the initial differential operator, we construct the Fourier transform. A connection between the convolution operation in the original functional space and the multiplication operation in the space of Fourier transforms is established. Finally, the problem on the convergence of spectral expansions generated by the original differential operator is studied. Examples of convolutions generated by operators are also presented.
34B05 , 34L05 , boundary form , boundary-value problem , convolution , differential operator , resolvent , spectral decomposition
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Al-Farabi Kazakh National University, Alma-Ata, Kazakhstan
Al-Farabi Kazakh National University
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