Related papers: Helffer-Sj{\"o}strand formula for Unitary Operator…

We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal…

A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on K\"ahler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure…

We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by Hausdorff operators is also considered.

We consider the indefinite Sturm-Liouville differential expression \[\mathfrak{a}(f) := - \frac{1}{w}\left( \frac{1}{r} f' \right)',\] where $\mathfrak{a}$ is defined on a finite or infinite open interval $I$ with $0\in I$ and the…

The Heun-Hahn operator on the uniform grid is defined. This operator is shown to map polynomials of degree $n$ to polynomials of degree $n+1$, to be tridiagonal in bases made out of either Pochhammer or Hahn polynomials and to be bilinear…

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J.…

Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a particular discrete symmetry. Applications to the PT-symmetric…

We give three formulas for meromorphic eigenfunctions (scattering states) of Sutherland's integrable N-body Schroedinger operators and their generalizations. The first is an explicit computation of the Etingof-Kirillov traces of…

We determine the low-energy behaviour of the scattering operator of two-dimensional Schr\"odinger operators with any type of obstructions at 0-energy. We also derive explicit formulas for the wave operators in the absence of p-resonances,…

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group…

The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.

A new geometric proof of the spectral theorem for unbounded self-adjoint operators A in a Hilbert space H is given based on a splitting of A in positive and negative parts A+ and A-. For both operators A+ and A- the spectral family can be…

Assume that $T_1,T_2$ are equivalent Schauder operators. In this paper, we show that even in this case their Schauder spectrum may be very different in the view of operator theory. In fact, we get that if a self-adjoint Schauder operator…

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…

We prove asymptotic formulas of Szeg\H{o} type for the periodic Schr\"odinger operator $H=-\frac{d^2}{dx^2}+V$ in dimension one. Admitting fairly general functions $h$ with $h(0)=0$, we study the trace of the operator…

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in…

In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both…

This paper delves into several characterizations of $A$-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates properties of the $A$-approximate point spectrum for the tensor…

In this paper, we establish results about operators similar to their adjoints. This is carried out in the setting of bounded and also unbounded operators on a Hilbert space. Among the results, we prove that an unbounded closed operator…

We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=…