Related papers: On the Fu/v cik spectrum with indefinite weights
We provide a complete description of the spectrum and the essential spectra of weighted composition operators $T=wT_\varphi$ on $C(K)$ in the case when the map $\varphi$ is a non-invertible homeomorphism of $K$ into itself.
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
In this article, we study the Fu\v{c}ik spectrum of fractional Laplace operator which is defined as the set of all $(\al,\ba)\in \mb R^2$ such that \begin{equation*} \quad \left. \begin{array}{lr} \quad (-\De)^s u = \al u^{+} - \ba u^{-} \;…
We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from…
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half…
Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.
We discuss an elementary problem in electrostatics: What does the charge distribution look like for a free charge on a strictly one-dimensional wire of finite length? To the best of our knowledge this question has so far not been discussed…
Finite dimensional linear spaces (both complex and real) with indefinite scalar product [.,.] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in…
In finite volume the partition function of QCD with a given $\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
Let X be a definable sub-set of some o-minimal structure. We study the spectrum of X, in relation with the definability of types.
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
Lattice QCD results on hadrons with heavy quarks are briefly reviewed. The focus is on the spectrum of conventional and exotic hadrons. Structure of certain conventional hadrons is addressed as well.
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
Cluster expansion methods are developed for calculating the spectral weight contributions of multiparticle excitations - continuum and bound states - to high orders. A complete 11th order calculation is carried out for the alternating…
We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non trivial integrable model.
Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic…
We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra $\mathbb{A}^n$. In the case $n=2$ we provide a detailed and, in most cases, complete description of these spectra.
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…