Konstantin Zhuikov

@rudn.ru

Assistant, S.M. Nikolskii Mathematical Institute
Peoples' Friendship University of Russia (RUDN University)

Konstantin Zhuikov


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https://researchid.co/zhuykovcon

RESEARCH INTERESTS

Elliptic theory, index theory, eta-invariant, nonlocal operators, periodic operators
9

Scopus Publications

Scopus Publications

  • On Two Methods of Determining η-Invariants of Elliptic Boundary-Value Problems
    K. N. Zhuikov, A. Yu. Savin
    Journal of Mathematical Sciences United States, 2025
  • On the Topological Index of Elliptic Operators on Two-Dimensional Manifolds with Cylindrical Ends
    H. H. Abbas, K. N. Zhuikov, A. Yu. Savin
    Mathematical Notes, 2024
    Abstract The topological index of elliptic operators on a two-dimensional manifold with cylindrical ends is constructed in terms of periodic cyclic cohomology of the algebra of symbols of these operators. The topological index for operators with shifts is constructed in the same way.
  • Eta-Invariant of Elliptic Parameter-Dependent Boundary-Value Problems
    K. N. Zhuikov, A. Yu. Savin
    Journal of Mathematical Sciences United States, 2024
  • -Invariant for Parameter-Dependent Boundary Value Problems
    A. Yu. Savin, K. N. Zhuikov
    Mathematical Notes, 2023
  • Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group
    K. N. Zhuikov, A. Yu. Savin
    Mathematical Notes, 2022
    $$\eta$$ -invariants for a class of parameter-dependent nonlocal operators associated with an isometric action of a discrete group of polynomial growth on a smooth closed manifold are studied. The $$\eta$$ -invariant is defined as the regularization of the winding number. The formula for the variation of the $$\eta$$ -invariant when the operator changes is obtained. The results are based on the study of asymptotic expansions of traces of parameter-dependent nonlocal operators.
  • Index of Differential-Difference Operators on an Infinite Cylinder
    K. N. Zhuikov
    Russian Journal of Mathematical Physics, 2022
    Differential-difference operators are considered on an infinite cylinder. The objective of the paper is to present an index formula for the operators in question. We define the operator symbol as a triple consisting of an internal symbol and conormal symbols on plus and minus infinity. The conormal symbols are families of operators with a parameter and periodic coefficients. Our index formula contains three terms: the contribution of the internal symbol on the base manifold, expressed by an analog of the Atiyah–Singer integral, the contributions of the conormal symbols at infinity, described in terms of the $$\eta$$ -invariant, and also the third term, which also depends on the conormal symbol. The result thus obtained generalizes the Fedosov–Schulze–Tarkhanov formula.
  • ETA-INVARIANT FOR PARAMETER-DEPENDENT FAMILIES WITH PERIODIC COEFFICIENTS
    Ufa Mathematical Journal, 2022
  • Elliptic Z-Operators Associated with the Metaplectic Group
    P. A. Sipailo, K. N. Zhuikov
    Russian Journal of Mathematical Physics, 2021
    In the paper, the ellipticity (Fredholm property) of operators of the form $$D_0+D_1\Phi$$ is investigated, where $$D_0, D_1$$ are pseudodifferential operators of Shubin type and $$\Phi$$ is a metaplectic operator, in Sobolev-type spaces on $$\mathbb{R}^N $$ . Explicit conditions for the ellipticity of such operators are given for the case in which the symplectic matrix associated with the operator $$\Phi$$ induces a topologically free action of the group $$\mathbb{Z}$$ on the sphere $$\mathbb{S}^{2N-1}$$ . The results thus obtained are applied to the inverse problem for the Schrödinger equation describing the dynamics of two noninteracting quantum systems for which the values of given observations at the initial and final times are known.
  • η-INVARIANT AND INDEX FOR OPERATORS ON THE REAL LINE PERIODIC AT INFINITY
    Anton Savin, , Konstantin Zhuikov, , and
    Eurasian Mathematical Journal, 2021