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Information × Registration Number 0123U100632, R & D request Title New analytical methods in inverse problems, operator theory, differential equations, as well as in functional equations on groups and ergodic theory Head Feldman Hennadii M., д.ф.-м.н. Registration Date 27-01-2023 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description1 The goal of research on the topic is the development of new analytical methods and their application in inverse problems, differential equations, as well as in functional equations on groups and ergodic theory. We plan to study inverse problems for differential operators of arbitrary order with nonlocal potentials. The main areas of research are solving the direct problem, that is, describing the spectrum, as well as solving the inverse problem, namely, restoring the nonlocal potential based on spectral data. We plan to develop, research and apply influence operators and transformation operators for the study of controllability problems for the wave equation and the heat conduction equation. We assume to apply the methods of complex analysis and the theory of evolutionary equations to the study of the asymptotic behavior of certain classes of strongly continuous semigroups of operators. We plan to study the issues of establishing the exact growth rate of the corresponding unbounded strongly continuous semigroups, the existence of their maximum asymptotics. We assume to study the solutions of functional equations, to which the proofs of characterization theorems on locally compact Abelian groups and on Banach spaces are reduces. We plan to continue the development of the theory of non-singular dynamic systems of probabilistic origin, primarily non-singular Poisson actions, as well as non-singular Bernoulli actions. In particular, we plan to study the connection between Krieger types of "basic" systems and their Poisson superstructures. We plan to study the unitary images of the inductive boundaries of symmetric groups relative to diagonal embeddings. popup.nrat_date 2024-12-09 Close