Related papers: Around operators not increasing the degree of poly…
Given a sequence of polynomials $(p_n)_n$, an algebra of operators $\mathcal{A}$ acting in the linear space of polynomials and an operator $D_p\in \mathcal{A}$ with $D_p(p_n)=np_n$, we form a new sequence of polynomials $(q_n)_n$ by…
We study Jacobi operators $J_{p}$, $p> -1$, whose eigenfunctions are Laguerre polynomials. All operators $J_{p}$ have absolutely continuous simple spectra coinciding with the positive half-axis. This fact, however, by no means imply that…
We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…
Consider an abstract operator $L$ which acts on monomials $x^n$ according to $L x^n= \lambda_n x^n + \nu_n x^{n-2}$ for $\lambda_n$ and $\nu_n$ some coefficients. Let $P_n(x)$ be eigenpolynomials of degree $n$ of $L$: $L P_n(x) = \lambda_n…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood…
Our aim is to study matrix polynomials over max-algebras and their growth in terms of a max-induced semi-norm. We investigate the relationship between the asymptotic growth of polynomial products and the joint spectral radius of the…
We analyze the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated K\"othe sequence spaces. We establish relationships with spaces of multipliers and apply these results…
We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that…
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non…
This paper, being the sequel of [An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators], studies a class of linear ordinary differential operators with polynomial coefficients called \emph{exactly solvable};…
Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…
We study basic spectral properties of J-self-adjoint $2\times 2$ block operator matrices. Using the linear resolvent growth condition, we obtain simple necessary conditions for the regularity of the critical point $\infty$. In particular,…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
This work studies operators mapping vector and scalar fields defined over a manifold $\mathcal{M}$, and which commute with its group of diffeomorphisms $\text{Diff}(\mathcal{M})$. We prove that in the case of scalar fields…
In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to…
We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant $J$-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation…