Related papers: On Abstract Spectral Constants

We investigate isoperimetric upper bounds for sums of consecutive Steklov eigenvalues of planar domains. The normalization involves the perimeter and scale-invariant geometric factors which measure deviation of the domain from roundness. We…

We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on…

We present a streamlined approach to relative oscillation criteria based on effective Pruefer angles adapted to the use at the edges of the essential spectrum. Based on this we provided a new scale of oscillation criteria for general…

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

We prove several results about the multiplicity of the first Steklov eigenvalues on compact surfaces with boundary. We improve some bounds on the multiplicity, especially for the first eigenvalue, and we prove they are sharp on some…

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…

We present an unified framework to identify spectra of Jacobi matrices. We give applications to long-standing conjecture of Chihara concerning one-quarter class of orthogonal polynomials, to the conjecture posed by Roehner and Valent…

In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. As an example, we demonstrate that a quadratic…

We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…

Given a collection of K\"ahler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equilibrium measures which coincide with classical notions when…

We develop tools to study arithmetically induced singular continuous spectrum in the neighborhood of the arithmetic transition in the hyperbolic regime. This leads to first transition-capturing upper bounds on packing and multifractal…

We provide a very general result that identifies the essential spectrum of broad classes of operators as exactly equal to the closure of the union of the spectra of suitable limits at infinity. Included is a new result on the essential…

We establish uncertainty principles on compact Riemannian manifolds without boundary by combining restriction estimates for orthonormal systems with spectral projection bounds for Laplace-Beltrami and Schr\"odinger operators. Our results…

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…

This article shows several new methods for proofs on Kan complexes while using them to give a compact introduction to the homotopy groups of these complexes. Then more advanced objects are studied starting with homology and the Hurewicz…

We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems ${\stackrel{\circ}{W}}\vphantom{W}_2^r(-1,1)\hookrightarrow{\stackrel{\circ}{W}}\vphantom{W}_\infty^k(-1,1)$ for various $r$ and $k$. The sharp…

Working with group homomorphisms, a construction of manifolds is introduced to preserve homology groups. The construction gives as special cases Qullien's plus construction with handles obtained by Hausmann, the existence of one-sided…

We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure…

We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of…