Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
21.07.1944
E-mail: Keywords: spectral theory of linear operators,
Banach algebras,
abstract harmonic analysis,
Banach modules,
differential equations in Banach spaces,
linear relations,
Linear differential operators,
spectrum of operators,
functional homogeneous spaces,
Green Function,
Fredholm operator,
Dirac operator,
spectrum asymptotic,
spectral distribution,
similar operators method.
Subject:
The spectral criteria for almost periodicity of abstract equations in Banach spaces were obtained. A new class of commutative Banach algebras with radical was introduced and studied. The spectral theory of Banach modules over such algebras was constructed. The method of similar operators for perturbed linear operators with discrete spectrum is developed. Estimates of the elements of the inverse matrix were obtained and applied to the spectral theory of linear operators. The spectral properties of abstract parabolic operators were studied by means of the methods of the theory operator semigroups. Basic elements of the spectral theory of linear relations (linear multivalued operators) were established and applied in the study of the degenerate differential equations.
Main publications:
Baskakov A. G. Spektralnye kriterii pochti periodichnosti reshenii funktsionalnykh uravnenii // Matematicheskie zametki, 1978. T. 24, # 2. S. 195–206.
Baskakov A. G. Spektralnyi analiz vozmuschennykh nekvazianaliticheskikh i spektralnykh operatorov // Izvestiya RAN, seriya matematicheskaya, 1994. T. 58, # 4. S. 3–32.
Baskakov A. G. Polugruppy raznostnykh operatorov v spektralnom analize lineinykh differentsialnykh operatorov // Funktsionalnyi analiz i ego prilozheniya, 1996. T. 30, # 3. S. 1–11.
Baskakov A. G. Otsenki elementov obratnykh matrits i spektralnyi analiz lineinykh operatorov // Izvestiya RAN, seriya matematicheskaya, 1997. T. 61, # 6. S. 3–26.
Baskakov A. G., Chernyshov K. I. Spektralnyi analiz lineinykh otnoshenii i vyrozhdennye polugruppy operatorov // Matematicheskii sbornik, 2002. T. 193, # 11. S. 3–35.
