Related papers: Spectral Sections

We study total and partial supersymmetry breaking by freely acting orbifolds, or equivalently by Scherk-Schwarz compactifications, in type I string theory. In particular, we describe a four-dimensional chiral compactification with…

For any vector bundle, we define an inverse system of spectra. In the case of a trivial bundle over a point, the homotopy groups of the filtration quotients give rise to the stable EHP spectral sequence, as was shown by Mahowald. The limit…

This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that…

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of $20$ topics in spectral graph theory,…

We consider discrete Schr\"odinger operators with real periodic potentials on periodic graphs. The spectra of the operators consist of a finite number of bands. By "rolling up" a periodic graph along some appropriate directions we obtain…

We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\mathcal{R}_s$-sectorial…

Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we intend to show that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.

The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this…

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 paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…

The spectra of massless Dirac operators are of essential interest e.g. for the electronic properties of graphene, but fundamental questions such as the existence of spectral gaps remain open. We show that the eigenvalues of massless Dirac…

Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…

In order to extend the spectral action principle to non-compact spaces, we propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. We show that an example is…

After introducing a natural notion of continuous fields of locally convex spaces, we establish a new theory of strongly continuous families of possibly unbounded self-adjoint operators over varying Hilbert spaces. This setting allows to…

In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.

Dirac-Schr\"{o}dinger systems play a central role when modeling Dirac bundles and Dirac-Schr\"{o}dinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. In this article we develop the Fredholm…

In 1992, Szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix $A$, based on the geometric symmetrization of powers of $A$. In 1998, Ta\c{s}\c{c}i and Kirkland proved a companion result by giving a…

We shall prove a convergence result relative to sequences of Minkowski symmetrals of general compact sets. In particular, we investigate the case when this process is induced by sequences of subspaces whose elements belong to a finite…

The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap of finite dimensional systems is given by Theorem 1.1, in terms…

We show the homological Serre spectral sequence with coefficients in a field is a spectral sequence of coalgebras. We also identify the comultiplication on the $E^2$ page of the spectral sequence as being induced by the usual…