In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

Abstract The Hilbert matrix $$\begin{aligned} {\mathcal {H}}_\lambda =\left( \frac{1}{n+m+\lambda }\right) _{n,m=0}^{\infty }, \quad \lambda \ne 0,-1,-2, \ldots \, \end{aligned}$$ H λ = <mml:mf...

The geometry of multi-parameter families quantum states is important in numerous contexts, including adiabatic or nonadiabatic dynamics, quenches, and the characterization critical points. Here, we discuss Hilbert-space eigenstates parameter-dependent random-matrix ensembles, deriving full probability distribution geometric tensor for Gaussian Unitary Ensemble. Our analytical results give exact...

In this paper, we compute the scattering matrix for the Hilbert modular group over any number field K. We then express the determinant of the scattering matrix as a ratio of completed Dedekind zeta functions associated to the Hilbert class field of K. This generalizes work of Efrat and Sarnak [ES] in the imaginary quadratic case.

In this talk we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert-Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert-Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Fin...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Motivated by a problem of scattering theory, the authors solve by quadratures a vector Riemann– Hilbert problem with the matrix coefficient of Chebotarev–Khrapkov type. The problem of matrix factorization reduces to a scalar Riemann–Hilbert boundary-value problem on a twosheeted Riemann surface of genus 3 that is topologically equivalent to a sphere with three handles. The conditions quenching ...

Let T be a block lower triangular contraction, i.e., a contractive operator T = (ti,j) ∞ i,j=−∞ acting from a doubly infinite Hilbert space direct sum ⊕∞ j=−∞Kj into a doubly infinite Hilbert space direct sum ⊕∞ j=−∞ Lj . The operator ti,j , which maps Kj into Li, is the (i, j)-th entry in the operator matrix representation of T relative to the natural Hilbert space direct sum decompositions. I...

Emmanuel Preissmann, Olivier Lévêque Swiss Federal Institute of Technology Lausanne, Switzerland Abstract In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic behaviour of the ...

This paper is concerned with the problem of finding a lower bound for certain matrix operators such as Hausdorff and Hilbert matrices on sequence spaces lp(w) and Lorentz sequence spaces d(w,p), which is recently considered in [7,8], similar to [13] considered by J. Pecaric, I. Peric and R. Roki. Also, this study is an extension of some works which are studied before in [1,2,7,8].