Related papers: Positive one-point commuting difference operators
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
We construct shift operators on equivariant symplectic cohomology which generalise the shift operators on equivariant quantum cohomology in algebraic geometry. That is, given a Hamiltonian action of the torus $T$, we assign to a cocharacter…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either…
Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the…
We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…
We relate non integer powers ${\mathcal L}^{s}$, $s>0$ of a given (unbounded) positive self-adjoint operator $\mathcal L$ in a real separable Hilbert space $\mathcal H$ with a certain differential operator of order $2\lceil{s}\rceil$,…
In this paper, we examine a specific class of quadratic operators. For these operators, we identified all fixed points and categorized their types in the general case. Our analysis revealed that there are no attractive fixed points except…
This paper shows that on the Bergman space of the open unit disk, the slant Toeplitz operator $T_{p+\varphi}$ and $T_{p+\psi}$ commute if and only if $\varphi=\psi$ ,where $\varphi$ and $\psi$ are both bounded analytic functions, and $p$ is…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
The paper has three parts. In the first part we apply the theory of commuting pairs of (pseudo) difference operators to the (formal) asymptotics of orthogonal polynomials: using purely geometrical arguments we show heuristically that the…
We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…
In this paper we characterize those positive operators which are asymptotic limits of contractions in strong operator topology or uniform topology. We examine the problem when the asymptotic limits of two contractions coincide.
Our goal is to extend the theory of the spectral shift function to the case where only the difference of some powers of the resolvents of self-adjoint operators belongs to the trace class. As an example, we consider a couple of Dirac…
In this paper, we complete the study of mapping properties for a family of operators evaluating the difference between differentiation operators and conditional expectations acting on noncommutative $L_{p}$-spaces. To be more precise, we…
We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.