Asymptotic of Eigenvalues of Pseudo-Differential Operators and Coulson-Type Integral Formulas with Common Hypercylic Functions

Abstract

The growth of frequently hypercyclic functions and common hypercyclic vectors for differential and translation operators and for the conjugate class of a hypercyclic operator and a Sot-Dense path of chaotic operators are studied. The spectral properties of the Cauchy process and asymptotic estimate of eigenvalues of pseudo-differential operators on half-line and interval with eigenvalues and refined semiclassical asymptotics for fractional Laplace operators, trace estimates and two-term estimates for unimodal Levy and relativistic stable processes are determined. We also classify the sum of powers of the Laplacian eigenvalues and normalized incidence energy of graphs with Coulson-type integral formulas for the general Laplacian-energy-like invariant of graphs.