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Showing papers in "Lobachevskii Journal of Mathematics in 2022"



























Journal ArticleDOI
TL;DR: In this paper , the authors studied the inverse spectral problems for Dirac-type functional-differential operators with constant delay and gave necessary and sufficient conditions for the solvability of these problems.
Abstract: We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For the considered case, however, we give answers to the full range of questions usually raised in the inverse spectral theory. Specifically, reconstruction of two complex $$L_{2}$$ -potentials is studied from either complete spectra or subspectra of two boundary value problems with one common boundary condition. We give conditions on the subspectra that are necessary and sufficient for the unique determination of the potentials. Moreover, necessary and sufficient conditions for the solvability of both inverse problems are obtained. For the inverse problem of recovering from the complete spectra, we establish also uniform stability in each ball of a finite radius. For this purpose, we use recent results on uniform stability of sine-type functions with asymptotically separated zeros.




DOI
TL;DR: A research method based on the use of DNC to solve basic elementary algorithms and analyzing the obtained characteristics of the model in comparison with classical algorithms for a Turing machine is proposed.