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pro vyhledávání: '"Shkalikov, A. A."'
Autor:
Kosarev, A. P., Shkalikov, A. A.
The aim of the paper is to find representation for solutions of $2\times 2$ system of ordinary differential equations $$ \mathbf{y^\prime} - B(x)\mathbf{y} = \lambda A(x)\mathbf{y}, \quad \ x \in [0, 1], $$ where $A(x) = diag\{a_1(x), a_2(x)\}$, $B(x
Externí odkaz:
http://arxiv.org/abs/2212.06227
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 smoothness indices are of different signs. This is done through the detail
Externí odkaz:
http://arxiv.org/abs/2212.05681
Autor:
Shkalikov, A. A., Tumanov, S. N.
We study the Sturm--Liouville operator $$ T(\varepsilon)y=-\frac{1}{\varepsilon}y''+ p(x)y, $$ with concrete $\mathcal{PT}$-- symmetric potential $p(x) = ix$ and Dirichlet boundary conditions on the segment $[-1,1]$. Here $\varepsilon \in (0, \infty)
Externí odkaz:
http://arxiv.org/abs/2112.03743
Autor:
Shkalikov, A. A.
This article can be considered as the first version of a book which the author plans to write about half-range problems in operator theory. It consists of two parts. The first part is based on lectures which the author delivered at University of Calg
Externí odkaz:
http://arxiv.org/abs/1912.04813
For $p > 1, \gamma \in \mathbb{R}$, denote by $H^{\gamma}_p(\mathbb{R}^n)$ the Bessel potential space, by $H^{\gamma}_{p, unif}(\mathbb{R}^n)$ the corresponding uniformly localized Bessel potential space and by $M[s, -t]$ the space of multipliers fro
Externí odkaz:
http://arxiv.org/abs/1912.03745
Autor:
Geynts, V. L., Shkalikov, A. A.
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 $q\in L_1((0,\infty), xdx)$, and asssume that the corresponding operator $H_q$ is defined by the Dirihlet condition $y(0)
Externí odkaz:
http://arxiv.org/abs/1912.03678
Autor:
Mirzoev, K. A., Shkalikov, A. A.
We work with differential expressions of the form \begin{align} \tau_{2n+1} y &=(-1)^ni \{(q_{0}y^{(n+1)})^{(n)}+(q_{0}y^{(n)})^{(n+1)}\}+ \sum\limits_{k=0}^{n}(-1)^{n+k}(p^{(k)}_ky^{(n-k)})^{(n-k)} \\ &\qquad+i\sum\limits_{k=1}^{n}(-1)^{n+k+1}\{(q^{
Externí odkaz:
http://arxiv.org/abs/1912.03660
Akademický článek
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Publikováno v:
Functional Analysis and Its Applications 53:3 (2019), 192-204
Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $\mathcal D(T)$. Assume that the spectrum of $T$ is confined in the union of disjoint intervals $\Delta_k =[\alpha_{2k-1},\alpha_{2k}]$, $k\in \mathbb{Z}$, and $$ \alpha_{2k+1}-\al
Externí odkaz:
http://arxiv.org/abs/1801.09789
Autor:
Belyaev, A. A., Shkalikov, A. A.
The objective of this paper is to describe the space of multipliers acting from a Bessel potential space $H^s_p(\mathbb R^n)$ into another space $H^{-t}_q(\mathbb R^n)$, provided that the smooth indices of these spaces have different signs, i.e. $s,
Externí odkaz:
http://arxiv.org/abs/1801.01830