Related papers: Explicit Formulas from the Continuous Spectrum

We extend the geometric side of Arthur's non-invariant trace formula for a reductive group $G$ defined over $\mathbb{Q}$ continuously to a natural space $\mathcal{C}(G(\mathbb{A}^1))$ of test functions which are not necessarily compactly…

A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…

Let $\gamma$ be an automorphism of a polarized complex projective manifold $(M,L)$. Then $\gamma$ induces an automorphism $\gamma_k$ of the space of global holomorphic sections of the $k$-th tensor power of $L$, for every $k=1,2,...$; for…

The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…

We present a method to derive the complete spectrum of the lift $\Gamma^\alpha$ of a base digraph $\Gamma$, with voltage assignments on a (finite) group $G$. The method is based on assigning to $\Gamma$ a quotient-like matrix whose entries…

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…

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…

Consider a topological surface $\Sigma$. We introduce the spectrum of a representation from the fundamental group of $\Sigma$ to SL(2,R), which is a subset of projective measured lamination on the surface, which captures the directions…

Let $F$ be a finite field of $char F > 3$ and $sl_{2}(F)$ be the Lie algebra of traceless $2\times 2$ matrices over $F$. This paper aims for the following goals: Find a basis for the $\mathbb{Z}_{2}$-graded identities of $sl_{2}(F)$; Find a…

In this paper we introduce a spectra preserving relation between graphs with loops and graphs without loops. This relation is achieved in two steps. First, by generalizing spectra results got on (m, k)-stars to a wider class of graphs, the…

The paper is devoted to the notion of a spectral section introduced by Melrose and Piazza. In the first part of the paper we generalize results of Melrose and Piazza to arbitrary base spaces, not necessarily compact. The second part…

Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory generated by the suspension spectra of smooth schemes. As a…

We explore an idea of Conrey and Li of expressing the Selberg trace formula as a Dirichlet series. We describe two applications, including an interpretation of the Selberg eigenvalue conjecture in terms of quadratic twists of certain…

We present a new and very short proof of the fact that, for positive $C_0$-semigroups on spaces of continuous functions, the spectral and the growth bound coincide. Our argument, inspired by an idea of Vogt, makes the role of the underlying…

Detecting and measuring repetitiveness of strings is a problem that has been extensively studied in data compression and text indexing. However, when the data are structured in a non-linear way, like in the context of two-dimensional…

Our aim is to show the way we pass from the results of ordered semigroups (or semigroups) to ordered $\Gamma$-semigroups (or $\Gamma$-semigroups). The results of this note have been transferred from ordered semigroups. The concept of…

The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018), arXiv:1802.01265]. We…

The goal of the paper "A new graph over semi-direct products of groups" is to define a graph \Gamma(G) on a group G when G splits over a normal subgroup. We demonstrate herein that the graph is ill-defined. We also attempt to ascertain…

We calculate the Wess-Zumino term $\Gamma(g)$ for a harmonic map $g$ of a closed surface to a compact, simply connected, simple Lie group $G$ in terms of the energy and the holonomy of the Chern-Simons line bundle on the moduli space of…

The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…