Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
24.12.1932
Keywords: linear differential operators; spectral theory; scattering; direct and inverse problems; finite and infinite systems of differential equations; eigenfunction expansions; spectral analysis; theory of extensions; deficiency indices; essential self-adjointness; oscillatory theory; the perturbations of spectra of the periodic or almost periodic operators.
Subject:
Direct and inverse (by a generalized V. A. Marchenko type spectral matrix) problems of spectral analysis for non-selfadjoint operator differnetial equations of second order were solved. An effective method of binary relations has been worked out and introduced to the theory of extensions of operators. The inverse Sturm–Liouville problem on the whole axis was solved. Perturbations of spectra for periodic and almost periodic operaotrs were investigated; Kneser type constants (critical constants) for each spectral gap were introduced. An expansion in eigenfunctions and a description of selfadjoint extensions for infinite systems of differential equations of arbitrary order were obtained. Also, for such systems an oscillation theory was produced (jointly with A. M. Kholkin). A broad class of conditions for essential selfadjointness for elliptic operators was obtained (jointly with A. G. Brusentsev and H. Kalf). A scattering theory on high singular potentials was worked out (jointly with E. H. Hristov). Inverse scattering problems for some classes of non-selfadjoint systems were solved (jointly with E. I. Bondarenko). There are some works on resolvent convergence and a generalization of the phase functions method.
Main publications:
Rofe–Beketov F. S. Deficiency indices and properties of spectrum of some classes of differential operators // Lecture Notes in Math., (Spectral theory and differential equations), 1975, 448, 273–293.
Rofe–Beketov F. S. The inverse Sturm–Liouville problem for the spectral matrix on the whole axis and associated problems // Pitman Research Notes in Math. Series 235. Longman Sci. and Techn. (Integral Equations and Inverse Problems, Ed. V. Petkov and R. Lazarov). 1991, 234–238.
