Related papers: Spectral Theory for $p$-adic Operators

Many authors have considered and investigated generalized fractional differential operators. The main object of this present paper is to define a new generalized fractional differential operator $\mathfrak{T}^{\beta,\tau,\gamma},$ which…

In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a…

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…

A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is presented for an adaptive spectral decomposition of self-adjoint…

This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems.…

Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…

The discrete spectrum of complex banded matrices which are compact perturbations of the standard banded matrix of order $p$ is under consideration. The rate of stabilization for the matrix entries sharp in the sense of order which provides…

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.

Using the differential precision methods developed previously by the same authors, we study the p-adic stability of standard operations on matrices and vector spaces. We demonstrate that lattice-based methods surpass naive methods in many…

For $0<r<1$, let us consider the following annulus: \[ \mathbb A_r= \{ z\in \mathbb C\, : \, r<|z|<1 \}. \] A Hilbert space operator $T$ for which $\overline{\mathbb A}_r$ is a spectral set is called an $\mathbb A_r$-\textit{contraction}.…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…

A matrix $A\in\mathbb{C}^{n\times n}$ is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every $A\in \mathbb{C}^{n\times n}$ is the limit of diagonalizable…

We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.

For a class of semilinear elliptic equations, we establish criteria that guarantee that the linearized operator associated with a solution satisfies certain spectral assumptions that are widely used in the analysis of the stability of…

A comparison is made between bispectral operator pairs and dual pairs of isomonodromic deformation equations. Through examples, it is shown how operators belonging to rank one bispectral algebras may be viewed equivalently as defining…

The main aims of this article are to characterize a class of operators associated with the symmetrized polydisc that admit rational dilations on the minimal space and to show an interplay between rational dilation and distinguished…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

We propose to build a combinatorial invariant, called the spectral monodromy, from the spectrum of a single non-selfadjoint h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from…