相关论文: Mixing property and pseudo random sequences
The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.
The notion of spectrum of first-order properties introduced by J. Spencer for Erdos-Renyi random graph is considered in relation to random uniform hypergraphs. We study properties of spectrum for first-order formulae with bounded quantifier…
The generalized spectral theory is an effective approach to analyze a linear operator on a Hilbert space $\mathcal{H}$ with a continuous spectrum. The generalized spectrum is computed via analytic continuations of the resolvent operators…
We discuss in which sense the so-called {\em regular pseudo-bosons}, recently introduced by Trifonov and analyzed in some details by the author, are related to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons}, and…
In this study, we apply "r" times the binomial transform to the Padovan and Perrin matrix sequences. Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we give the…
Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that…
The repetition property of a sequence in a metric space, a notion introduced by us in an earlier paper, is of importance in the spectral analysis of ergodic Schr\"odinger operators. It may be used to exclude eigenvalues for such operators.…
In this note, we introduce and study the left (right) pseudospectrum and left (right) condition pseudospectrum of bounded linear operators on ultrametric Banach spaces. We prove some results about them.
In this paper, we investigate the properties of q-Hermite polynomials related to q-Bernstein polynomials. From these properties, we derive some interesting relations between q-Berstein polynomials and q-Hermite polynomials.
We study the spectrum of single-photon emission and scattering in a mixed optomechanical model which consists of both linear and quadratic optomechanical interactions. The spectra are calculated based on the exact long-time solutions of the…
We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…
A cycle expansion technique for discrete sums of several PF operators, similar to the one used in standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an…
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated…
We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator…
We construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
We study relations between spectra of two operators that are connected to each other through some intertwining conditions. As application we obtain new results on the spectra of multiplication operators on $B(\cl H)$ relating it to the…
For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions…
The relation between the spectra of operator pencils with unbounded coefficients and of associated linear relations is investigated. It turns out that various types of spectrum coincide and the same is true for the Weyr characteristics.…
We show that any $L^2$-bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and $L^2$-spectrum for rational functions. Based on this observation, we also…