Zobrazeno 1 - 10
of 221
pro vyhledávání: '"47a06"'
Autor:
Jursenas, Rytis
It is a classical result that, if a maximal symmetric operator $T$ in a Krein space $\mathcal{H}=\mathcal{H}^-[\oplus]\mathcal{H}^+$ has the property $\mathcal{H}^-\subseteq\mathcal{D}_T$, then the imaginary part of its eigenvalue $\lambda$ from uppe
Externí odkaz:
http://arxiv.org/abs/2410.16725
Autor:
Wang, Yicao
Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl functions. We pr
Externí odkaz:
http://arxiv.org/abs/2408.10968
Autor:
Xu, Guixin, Ren, Guojing
This paper investigates quasi-selfadjoint extensions of dual pairs of linear relations in Hilbert spaces. Some properties of dual pairs of linear relations are given and an Hermitian linear relation associated with a dual pair of linear relations is
Externí odkaz:
http://arxiv.org/abs/2404.02355
The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator
Eigenvalue interlacing is a useful tool in linear algebra and spectral analysis. In its simplest form, the interlacing inequality states that a rank-one positive perturbation shifts each eigenvalue up, but not further than the next unperturbed eigenv
Externí odkaz:
http://arxiv.org/abs/2311.06701
Autor:
Hassi, Seppo, de Snoo, Henk
A semibounded operator or relation $S$ in a Hilbert space with lower bound $m \in {\mathbb R}$ has a symmetric extension $S_{\rm f}=S {\, \widehat + \,} (\{0\} \times {\rm mul\,} S^*)$, the weak Friedrichs extension of $S$, and a selfadjoint extensio
Externí odkaz:
http://arxiv.org/abs/2403.19041
Autor:
Hassi, Seppo, de Snoo, Henk
In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type decomposition
Externí odkaz:
http://arxiv.org/abs/2308.09408
Autor:
Rios-Cangas, Josué I.
The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and symmetric contractions. It is treated with a slight variation of the usual one, resulting in an involution fo
Externí odkaz:
http://arxiv.org/abs/2308.06400
Autor:
Borogovac, Muhamed
Given Krein and Hilbert spaces $\left( \mathcal{K},[.,.] \right)$ and $\left( \mathcal{H}, \left( .,. \right) \right)$, respectively, the concept of the boundary triple $\Pi =(\mathcal{H}, \Gamma _{0}, \Gamma_{1})$ is generalized through the abstract
Externí odkaz:
http://arxiv.org/abs/2307.15954
Autor:
Silva, Luis O., Toloza, Julio H.
A de Branges space $\mathcal B$ is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map $F(z) \mapsto F(-z)$. Let $K_\mathcal{B}(z,w)$ be the reproducing kernel in $\math
Externí odkaz:
http://arxiv.org/abs/2304.13127
Autor:
Jursenas, Rytis
It is a classical result that the Weyl function of a simple symmetric operator in a Hilbert space determines a boundary triple uniquely up to unitary equivalence. We generalize this result to a simple symmetric operator in a Pontryagin space, where u
Externí odkaz:
http://arxiv.org/abs/2303.04601