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

We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies. Given a labeled dataset encoded in a one-hot…

In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…

The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it…

The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…

The main goal of this thesis is to show the crucial role that plays the symbol in analysing the spectrum the sequence of matrices resulting from PDE approximation and in designing a fast method to solve the associated linear problem. In the…

The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some…

The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…

We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any…

The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…

Normality of bounded and unbounded adjointable operators are discussed. Suppose $T$ is an adjointable operator between Hilbert C*-modules which has polar decomposition, then $T$ is normal if and only if there exists a unitary operator $…

We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the…

Let $\mathcal{H}$ be a separable infinite-dimensional complex Hilbert space, $\mathcal{B}(\mathcal{H})$ the algebra of bounded linear operators acting on $\mathcal{H}$ and $\mathcal{J}$ a proper two-sided ideal of…

This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the…

In this paper, we mutuate the concept of Ducci matrices to the $p$-adic setting, generalizing the classical Ducci sequences to the framework of $p$-adic numbers. The classical Ducci operator, which iteratively computes the absolute…

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of $S$-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and…

In this paper we continue to study the degrees of matrix coefficients of intertwining operators associated to reductive groups over $p$-adic local fields. Together with previous analysis of global normalizing factors we can control the…

Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…