A. Shkalikov

activity

20022022

most citedBounds on variation of spectral subspaces under J-self-adjoint perturbations

32 citations · 72 across the 24 of their papers we have counts for

collaborators

24 papers

math.FA2022

Multipliers in the scale of periodic Bessel potential spaces with smoothness indices of different signs

Alexei A. Belyaev, Andrei A. Shkalikov

We prove a general type description result for the multipliers acting between two periodic Bessel potential spaces, defined on the $n$ --dimensional torus, in a case when their smoo…

math.SP2021

The Complex Airy Operator as Explicitly Solvable PT-symmetrical Model

A. A. Shkalikov, S. N. Tumanov

We study the Sturm--Liouville operator $T (ε) y = - \frac{1}{ε} y^{''} + p (x) y,$ with concrete $P T$ -- symmetric potential $p (x) = i x$ and Dirichlet boundary…

math.FA2019

Sharp embeddings of uniformly localized Bessel potential spaces into multiplier spaces

Alexei A. Belyaev, Andrei A. Shkalikov

For $p > 1, γ \in R$ , denote by $H_{p}^{γ} (R^{n})$ the Bessel potential space, by $H_{p, u ni f}^{γ} (R^{n})$ the corresponding uniformly localized Bessel potential sp…

math.SP2019

Stability in the inverse resonance problem for the Schr\" odinger operator

V. L. Geynts, A. A. Shkalikov

We work with the Schr\" odinger equation \begin{equation*} H_q y = -y'' + q(x)y = z^2y, \ x\in [0,\infty), \end{equation*} where $q \in L_{1} ((0, \infty), x d x)$ , and asssume that the c…

math.SP2018★ 2 cited

Preserving of the unconditional basis property under non-self-adjoint perturbations of self-adjoint operators

Alexander K. Motovilov, Andrei A. Shkalikov

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $D (T)$ . Assume that the spectrum of $T$ is confined in the union of disjoint intervals $Δ_k =[α_{2k-1…

math.FA2018

Multipliers in Bessel potential spaces. The case of different sign smooth indices

A. A. Belyaev, A. A. Shkalikov

The objective of this paper is to describe the space of multipliers acting from a Bessel potential space $H_{p}^{s} (R^{n})$ into another space $H_{q}^{- t} (R^{n})$ , provided t…