Related papers: Spectra of stationary processes on Z
Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…
In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set is periodic, with the period an integral multiple of the measure of the set. As a…
We study the persistence probability of a centered stationary Gaussian process on $\mathbb{Z}$ or $\mathbb{R}$, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the…
We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…
Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at $0$, known to hold for bounded scalar type spectral…
We consider discrete periodic operator on $\mathbb Z^d$ with respect to lattices $\Gamma\subset\mathbb Z^d$ of full rank. We describe the class of lattices $\Gamma$ for which the operator may have a spectral gap for arbitrarily small…
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the…
We consider the first order periodic systems perturbed by a $2N\ts 2N$ matrix-valued periodic potential on the real line. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the…
A theorem of A. and C. R\'enyi on periodic entire functions states that an entire function $f(z) $ must be periodic if $ P(f(z)) $ is periodic, where $ P(z) $ is a non-constant polynomial. By extending this theorem, we can answer some open…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding…
The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
In this work, we consider the periodic impulse control of a system modeled as a set of linear differential equations. We define a matrix that governs the qualitative behavior of the controlled system. This matrix depends on the period and…
We give necessary and sufficient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes.
In this paper we find explicit conditions on the periodic PT-symmetric complex-valued potential q for which the number of gaps in the real part of the spectrum of the one-dimensional Schrodinger operator L(q) is finite.
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We study the probability of a real-valued stationary process to be positive on a large interval $[0,N]$. We show that if in some neighborhood of the origin the spectral measure of the process has density which is bounded away from zero and…
For a monadic sentence psi in the finite vocabulary we show that the spectra, the set of cardinalities of models of psi is almost periodic under reasonable conditions. The first is that every model is so called ``weakly k-decomposable''.…