Related papers: Isospectral operators
In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the…
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
We consider the Dirichlet realization of the operator $-h^2\Delta+iV$ in the semi-classical limit $h\to0$, where $V$ is a smooth real potential with no critical points. For a one dimensional setting, we obtain the complete asymptotic…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…
The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are…
It is by now well known that the wave functions of rational solutions to the KP hierarchy (those which can be achieved as limits of the pure n-soliton solutions) satisfy an additional eigenvalue equation for ordinary differential operators…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
Second-order variational properties have been shown to play important theoretical and numerical roles for different classes of optimization problems. Among such properties, twice epi-differentiability has a special place because of its…
We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…
In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
A general scheme for tridiagonalising differential, difference or q-difference operators using orthogonal polynomials is described. From the tridiagonal form the spectral decomposition can be described in terms of the orthogonality measure…
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates…
In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
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 relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum. We also obtain a constructive procedure…