Related papers: Regularity of the spectrum for expanding maps
The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau--Weyl pseudodifferential…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
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 behaviour of the solutions of the stationary diffusion equation as a function of a possibly rough ($L^{\infty}$-) diffusivity. This includes the boundary behaviour of the solution maps, associating to each diffusivity the…
M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for…
A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed…
We obtain an operator algebraic characterization for when we can continuously extend the shift map from a standard countable Markov shift $\Sigma_A$ to its respective generalized countable Markov shift $X_A$ (a compactification of…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to…
We study the spectral properties of a family of generalized transfer operators associated to the Farey map. We show that when acting on a suitable space of holomorphic functions, the operators are self-adjoint and the positive dominant…
In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…
We consider an eigenvalue problem for an inverted one dimensional harmonic oscillator. We find a complete description for the eigenproblem in $C^{\infty}(\mathbb R)$. The eigenfunctions are described in terms of the confluent hypergeometric…
We investigate a random normal matrix model with eigenvalues forced to be in the droplet, the support of the equilibrium measure associated with an external field. For radially symmetric external fields, we show that the fluctuations of the…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…