Search academic texts

Information × Registration Number 0223U002269, 0118U003110 , R & D reports Title Methods of the functions theory in spectral theory, control theory, functional equations, ergodic theory, and representation theory popup.stage_title Head Feldman Hennadii M., д.ф.-м.н. Registration Date 14-02-2023 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2 New Blaschke-type conditions for the distribution of the roots of analytic functions of non-radial growth were obtained and this result was applied to describe the discrete spectrum of non-self-adjoint perturbations of the bilayer graphene operator. Calculated spectra of new classes of counted graphs. Model images of the roots of operator non-self-adjoint quadratic bundles are constructed; solved the inverse problem for the operator with nonlocal potential. The data of the inverse problem for the operator with nonlocal potential are described. The inverse spectral problem for the self-adjoint operator of the third derivative with a nonlocal potential is solved. New orthonormal bases of the corresponding Sobolev spaces were constructed for the heat conduction equation with constant coefficients on the semi-axis, governed by the Dirichlet or Neumann boundary condition, and the heat conduction equation on the half-plane, governed by the Dirichlet boundary condition with point control. The accuracy of the spectral XYZ theorem is proved. New generalizations of the characterization theorems of Skitovich-Darmois, Heyde, Rao, and Poya for various classes of locally compact abelian groups are obtained. Necessary and sufficient conditions for the recurrence of random walks on subgroups of the group of rational numbers have been obtained. A class of transformations of rank one with infinite invariant measure and the property of minimal Radon autojoinings is constructed. Weak mixing is proved for a wide class of conservative nonsingular Bernoulli actions. It is proved that typical nonsingular Poisson superstructures are of Krieger type III1. The Lemanchyk-Lesin-Skrenty hypothesis regarding the ergodicity of conservative Gaussian cocycles for mildly mixing Gaussian transformations is confirmed. The criteria for the properties of Haagerup and the Khazdan pair in terms of ergodic actions preserving infinite measure are established.  Product Description popup.authors popup.nrat_date 2023-02-14 Close