Related papers: Spectral Sets
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
Finite rank perturbations $T=N+K$ of a bounded normal operator $N$ on a separable Hilbert space are studied thanks to a natural functional model of $T$; in its turn the functional model solely relies on a perturbation matrix/ characteristic…
Gramsch and Lay [10] gave spectral mapping theorems for the Dunford-Taylor calculus of a closed linear operator $T$, $$\widetilde{\sigma}_i(f(T)) = f(\widetilde{\sigma}_i(T)), $$ for several extended essential spectra…
The spectrum of the infinite dimensional Neumann matrices M^{11}, M^{12} and M^{21} in the oscillator construction of the three-string vertex determines key properties of the star product and of wedge and sliver states. We study the…
Analyses of stellar spectra often begin with the determination of a number of parameters that define a model atmosphere. This work presents a prototype for an automated spectral classification system that uses a 15 nm-wide region around…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
It is possible to enumerate all computer programs. In particular, for every partial computable function, there is a shortest program which computes that function. f-MIN is the set of indices for shortest programs. In 1972, Meyer showed that…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non trivial integrable model.
The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
This article proposes a framework for the study of periodic maps $T$ from a (typically finite) set $X$ to itself when the set $X$ is equipped with one or more real- or complex-valued functions. The main idea, inspired by the time-evolution…
We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the…
Spectral analysis is a powerful tool, decomposing any function into simpler parts. In machine learning, Mercer's theorem generalizes this idea, providing for any kernel and input distribution a natural basis of functions of increasing…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
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 present a novel approach to the representation theory of finite dimensional algebras motivated by the emerging theory of graph limits. We introduce the rank spectrum of a finite dimensional algebra $R$ over a finite field. The elements…
Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the…
The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…