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101.
We propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator where p > 0 is a strictly positive function. Denote by the orthogonal projection of Ap corresponding to the spectrum of Ap in ; the range of this projection is the space of functions of variable bandwidth with spectral set in Λ. We will develop the basic theory of these function spaces. First, we derive (nonuniform) sampling theorems; second, we prove necessary density conditions in the style of Landau. Roughly, for a spectrum the main results say that, in a neighborhood of , a function of variable bandwidth behaves like a band‐limited function with local bandwidth . Although the formulation of the results is deceptively similar to the corresponding results for classical band‐limited functions, the methods of proof are much more involved. On the one hand, we use the oscillation method from sampling theory and frame‐theoretic methods; on the other hand, we need the precise spectral theory of Sturm‐Liouville operators and the scattering theory of one‐dimensional Schrödinger operators. © 2017 Wiley Periodicals, Inc. 相似文献
102.
We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay. 相似文献
103.
V. A. Andreev D. M. Davidović L. D. Davidović Milena D. Davidović Miloš D. Davidović 《Theoretical and Mathematical Physics》2017,192(1):1080-1096
We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states. 相似文献
104.
A. Laurinčikas R. Macaitienė 《Proceedings of the Steklov Institute of Mathematics》2017,299(1):143-156
The Selberg class S consists of functions L(s) that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in S that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts L(s + iτ ), τ ∈ R. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts L(s + ikh), k = 0, 1,..., where h > 0 is an arbitrary fixed number. 相似文献
105.
Stability,periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory 下载免费PDF全文
Mirela Garić‐Demirović M. Nurkanović Z. Nurkanović 《Mathematical Methods in the Applied Sciences》2017,40(1):306-318
By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation where A ,B ,D > 0,u ?1,u 0>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
106.
František Kačík Jana Luptáková Pavel Šmíra Adriana Eštoková Danica Kačíková Andrea Nasswettrová Tatiana Bubeníková 《Journal of Thermal Analysis and Calorimetry》2017,128(2):755-764
Glasses having composition 5Li2O–5ZnO– xBi2O3 –(90 ? x) P2O5 (x = 5, 10, 15, 20 and 25 mol%) were prepared by the normal melt quenching technique. Nanocomposite glass containing bismuth phosphate BiPO4 nanocrystals was obtained, which can be attributed to homogeneous nucleation process. The formation of BiPO4 nanocrystals was confirmed and characterized by X-ray diffraction patterns (XRD), transmission electron microscopy (TEM), differential scanning calorimetry, optical absorption (UV–Vis) and micro-hardness studies. The morphological analysis by XRD and TEM microscopy showed the formation of hexagonal BiPO4 nanocrystals, and its estimated nanocrystalline sizes were found to be varying from 5.35 to 11.53 nm depending on the Bi2O3 concentrations. The density (ρ) and molar volume (V m) were also determined and found to be in compositional dependence. Glass transition temperature (T g) and glass crystallization temperature (T c) were obtained and found to be increased (from 240.0 to 337.2 °C) with increasing Bi2O3 up to 20 mol% and then decreased (from 337.2 to 331.8 °C) due to the structural changes in the glass network. Effect of BiPO4 content on the optical properties had been investigated. From the UV–Vis spectra, it was observed that the fundamental absorption edge shifts toward lower wavelengths, i.e., blueshifts with increasing Bi2O3 mol% up to 20 mol%, and then shifts toward higher wavelengths, i.e., redshifts beyond 20 mol%. It was also observed that the obtained E opt (for indirect and direct transitions) increases with gradual increase in Bi2O3 content up to 20 mol% and then decreases beyond 20 mol%. This may be due to the introduction of Bi cations into the glass network as a network former up to 20 mol% causing a decrease in ΔE values, beyond 20 mol%, the introduction of Bi ions into the glass network interstitially leads to increase the values of ΔE. The optical properties of the present nanocrystallized glasses showed a quantum size dependence, in which the optical band gap energy (E opt) was changed as a function of BiPO4 nanocrystalline sizes. 相似文献
107.
For most values of parameters λ and α, the zeros of the Lerch zeta-function L(λ, α, s) are distributed very chaotically. In this paper, we consider the particular case of equal parameters L(λ, λ, s) and show by calculations that the nontrivial zeros either lie extremely close to the critical line σ = 1/2 or are distributed almost symmetrically with respect to the critical line. We also investigate this phenomenon theoretically. 相似文献
108.
Vladimir Piterbarg Goran Popivoda Siniša Stamatović 《Lithuanian Mathematical Journal》2017,57(1):128-141
Let ξ(t), t ∈ [0, T],T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η(t) and μ(t) be other sufficiently smooth random processes independent of ξ(t). In this paper, we obtain an asymptotic exact result for P(sup t∈[0,T](η(t)ξ(t) + μ(t)) > u) as u→∞. 相似文献
109.
Mihajlo Cekić 《偏微分方程通讯》2017,42(11):1781-1836
In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy. 相似文献
110.