On a Q-boundary value problem with discontinuity conditions
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In this paper, we studied q-analogue of Sturm-Liouville boundary value problem on a finite interval having a discontinuity in an interior point. We proved that the q-Sturm-Liouville problem is self-adjoint in a modified Hilbert space. We investigated spectral properties of the eigenvalues and the eigenfunctions of q-Sturm-Liouville boundary value problem. We shown that eigenfunctions of q-Sturm-Liouville boundary value problem are in the form of a complete system. Finally, we proved a sampling theorem for integral transforms whose kernels are basic functions and the integral is of Jackson’s type.
Q-sturm-liouville operator, self-adjoint operator, completeness ofeigenfunctions, sampling theory
Короткий адрес: https://sciup.org/147236520
IDR: 147236520 | DOI: 10.14529/mmph210401
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