Main results
The theory of subharmonic majorants has been built.
The theory of representations of positive polynomials, related to
generalizations of Hermite-Bieler theorem and Fejer-Riesz theorem, has been
worked out.
The theory of interpolational problems on normed spaces of entire
functions has been built.
The theory of distribution of values of meromorphic functions on
arguments has been worked out.
Arithmetic of multivariate probability distributions has been built.
Spectral theory of self-adjoint and not self-adjoint Hill's operators
has been built.
Nonquasianalytic representations of locally compact abelian groups in
Banach space is studied.
The theory of growth and distribution of zeros of entire functions of
several variables has been built.
The theory of entire functions of completely regular growth of several
variables has been built.
The theory of holomorphic almost-periodic mappings of several variables
and associated flows has been worked out.
The problem of spectral synthesis for generalized folding operators on
the spaces of entire functions has been solved.
The theory of Fourier series for Hardy spaces in convex domains has been
built.
The problems of completeness, minimality and summarization of
decompositions for the exponential systems in the spaces of the functions on
the curves have been solved.
The theory of stability of decompositions of probability distributions
has been built.
Arithmetic of probability distributions on locally compact Abelian
groups has been built.
The theory of distribution of values of meromorphic functions on the
basis of potential theory has been built.
The classical problem of description of algebraic differential equations
having meromorphic solutions has been solved.
The complete solution of the problem of recovery of Hill's operator's
spectrum in the classes of quasianalytic functions has been obtained.
The theory of operators subharmonicity-preserving has been worked out.
Algebraic solutions of classical problems of Chebyshev's type have been
obtained.
The analogs of the characterization theorems by Bernstein,
Skitovich-Darmois and Heyde have been obtained for
various
classes of
locally compact Abelian groups, in particular for the additive group of the
field of p-adic numbers.
The spectral theory of orthogonal polynomial on the unit circle has been
built.
It was investigated the connection between polynomial asymptotic
representation of a subharmonicfunction in the plane and the function of
distribution of its Riesz measure.
The theory of zero (Riesz measure) distribution for analytic (subharmonic)
functions of nonradial growth in the unit disk, with applications in the
spectral theory of non-selfadjoint operators has been built.
Model representations of Lie algebras of linear non-self-adjoint
operators are constructed.
Model representations of commutative systems of non-unitary operators
are constructed.
Theory of inverse problems (spectral and scattering) for differential
operators with non-local potentials is constructed.
Modified spaces of the Sobolev type generated by second-order
differential operators with variable coefficients were constructed and
studied.
Transformation operators for second-order differential operators with
variable coefficients were constructed on the base of the classic
transformation operators for the Sturm-Liouville problem, The constructed
operators were investigated and applied to control problems.
The theory of nonsingular Poisson suspensions was developed.