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pro vyhledávání: '"Malamud Mark A"'
In recent joint papers the authors of this note solved a famous problem remained open for many years and proved that for arbitrary contractions with trace class difference there exists an integrable spectral shift function, for which an analogue of t
Externí odkaz:
http://arxiv.org/abs/2410.22529
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the completeness property of the system of root vectors of a boundary value problem for the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad y= {\rm col}(y_1, y_2), \quad x \in
Externí odkaz:
http://arxiv.org/abs/2312.15933
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the following $n\times n$ Dirac type equation$$Ly=-iB(x)^{-1}(y'+Q(x)y)=\lambda y, \quad B(x)=B(x)^*,\quad y={\rm col}(y_1,\ldots,y_n),\quad x\in[0,\ell],$$ on a finite interval $[0,\ell]$. Here $Q$ is a summable potential
Externí odkaz:
http://arxiv.org/abs/2112.07248
Publikováno v:
Adv. Math., vol. 395, ID 108158 (2022)
The Glazman-Povzner-Wienholtz theorem states that the completeness of a manifold, when combined with the semiboundedness of the Schr\"odinger operator $-\Delta + q$ and suitable local regularity assumptions on $q$, guarantees its essential self-adjoi
Externí odkaz:
http://arxiv.org/abs/2105.09931
Autor:
Budyka, Viktoriya, Malamud, Mark
The paper concerns with infinite symmetric block Jacobi matrices $\bf J$ with $p\times p$-matrix entries. We present new conditions for general block Jacobi matrices to be selfadjoint and have discrete spectrum. In our previous papers there was estab
Externí odkaz:
http://arxiv.org/abs/2012.15578
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with the stability property under perturbation $Q\to\widetilde Q$ of different spectral characteristics of a BVP associated in $L^2([0,1];\Bbb C^2)$ with the following $2\times2$ Dirac type equation $$L_U(Q)y=-iB^{-1}y'+Q(x)y=\
Externí odkaz:
http://arxiv.org/abs/2012.11170
Let $\mathcal{G}$ be a metric noncompact connected graph with finitely many edges. The main object of the paper is the Hamiltonian ${\bf H}_{\alpha}$ associated in $L^2(\mathcal{G};\mathbb{C}^m)$ with a matrix Sturm-Liouville expression and boundary
Externí odkaz:
http://arxiv.org/abs/2012.03097
Autor:
Lunyov, Anton A., Malamud, Mark M.
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 March 2025 543(2) Part 1
Autor:
Lunyov, Anton A., Malamud, Mark M.
The paper is concerned with completeness property of rank one perturbations of unperturbed operators generated by special boundary value problems (BVP) for the following $2 \times 2$ system \begin{equation} L y = -i B^{-1} y' + Q(x) y = \lambda y , \
Externí odkaz:
http://arxiv.org/abs/1807.05345
In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the absolute continuity of spectral shift, we us
Externí odkaz:
http://arxiv.org/abs/1802.10243