Related papers: Spectral Theory for $p$-adic Operators
This paper studies the delocalized regime of an ultrametric random operator whose independent entries have variances decaying in a suitable hierarchical metric on $\mathbb{N}$. When the decay-rate of the off-diagonal variances is…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
This paper explores operators with countable, continuous, and hybrid spectra, focusing on both finite dimensional and infinite dimensional cases, particularly in non-Hermitian systems. For finite dimensional operators, a novel concept of…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
We present a new proof of results of Kurdyka & Paunescu, and of Rainer, about real-analytic multi-parameters generalizations of classical results by Rellich and Kato about the reduction in families of univariate deformations of normal…
In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
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…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is…
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on…
New orthonormal basis of eigenfunctions for the Vladimirov operator of p-adic fractional derivation is constructed. The map of p-adic numbers onto real numbers (p-adic change of variables) is considered. This map (for p=2) provides an…
The theory of quaternionic operators has applications in several different fields such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^p$-norm can be upper bounded, up to an asymptotically small error, by the operator norm of the same polynomial evaluated in free…
We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…
We consider the Schur-Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is…