About 70 scientific publications with results in the following fields: Methods of summation of divergent series, a theorem on the consistence (1953–54). Partial differential equations with constant coefficients, the existence of solutions and the construction of general solutions in some classes of usual functions and distributions, atest for smoothness of a d eneralized solution in a bounded domain (1958–61). General boundary value problems for elliptic systems, the equivalence of the ellipticity and of the Fredholm property of pseudodifferential boundary value problems; relative index theorems; the unique solvability of problems elliptic with parameter (1962–65). General mixed boundary value problems for parabolic systems in a cylindrical domain, the unique solvability (1963–67). Positive boundary value problems for symmetric and symmetrizable first order systems, the Fredholm property and the unique solvability (1966–69). General mixed boundary value problem for hyperbolic first order systems in a cylindrical domain with the uniform Lopatinskii condition, the development of the results due to Kreiss on the unique solvability (1971–72). Non-standard spectral problems for the Helmholtz equation and the Maxwell system, the basis property of the eigenfunctions and the completeness of the root functions, the localization and the asymptotic behavior of eigenvalues (1973–77). Non-self-adjoint operators that are weak perturbations of self-adjoint ones and operators far from being self-adjoint, the summability of Fourier series with respect to the root functions and the behavior of the eigenvalues (1976–92). Elliptic pseudo-differential operators on a closed curve, similarity transforms and asymptotic series for the eigenvalues and the eigenfunctions (1979–84). Relations between functions of an elliptic pseudodifferential operator, the asymptotics of the kernel of the resolvent with logarithmic terms, spectral asymptotics (1987–92). Spectral elliptic boundary value problems in Lipschitz domains, the investigation of the spectrum and the properties of the eigenfunctions and the root functions (the smoothness, the completeness and the basis property) (1994–2001). The analysis of the spectral approaches to the construction of the $R$-matrix for the Schrodinger equation and the Dirac system (2001). Collaborated and wrote common papers with the following mathematicians: M. I. Vishik, A. S. Dynin, Z. N. Golubeva, A. S. Markus, B. A. Amosov, M. Faierman, R. Denk, R. Mennicken, M. Levitin. Common book with physicists B. Z. Katsenelenbaum, A. N. Sivov, and N. N. Voitovich. See details in the note in Russian Mathematical Surveys, 2001, 56(4), 163–168. Variational elliptic boundary value problems in Lipschitz domains.
Spectral problems.
Pseudodifferential operators with nonsmooth symbols or kernels.
Main publications:
M. C. Agranovich, “Spektralnye zadachi dlya silno ellipticheskikh sistem vtorogo poryadka v oblastyakh s gladkoi i negladkoi granitsei”, UMN, 57:5 (2002), 3–78
M. C. Agranovich, “Operatory tipa potentsiala i zadachi sopryazheniya dlya silno ellipticheskikh sistem 2-go poryadka v oblastyakh s lipshitsevoi granitsei”, Funktsionalnyi analiz i ego prilozheniya, 43:3 (2009), 3–25
