共查询到20条相似文献,搜索用时 15 毫秒
1.
Ole Christensen Augustus J. E. M. Janssen Hong Oh Kim Rae Young Kim 《Advances in Computational Mathematics》2018,44(5):1519-1535
It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function. 相似文献
2.
In this paper, we prove a Scattering theorem for the wave equation with localized subcritical semilinearity outside convex obstacle; then we deduce the exponential decay of local energy. The proof relies on generalized Strichartz estimates, and microlocal defect measures.Mathematics Subject Classification (2000): 35B35, 35L05in final form: 09 October 2003 相似文献
3.
4.
Gabor frames, unimodularity, and window decay 总被引:4,自引:0,他引:4
We study time-continuous Gabor frame generating window functions g satisfying decay properties in time and/or frequency with
particular emphasis on rational time-frequency lattices. Specifically, we show under what conditions these decay properties
of g are inherited by its minimal dual γ0 and by generalized duals γ. We consider compactly supported, exponentially decaying, and faster than exponentially decaying
(i.e., decay like |g(t)|≤Ce−α|t|
1/α for some 1/2≤α<1) window functions. Particularly, we find that g and γ0 have better than exponential decay in both domains if and only if the associated Zibulski-Zeevi matrix is unimodular, i.e.,
its determinant is a constant. In the case of integer oversampling, unimodularity of the Zibulski-Zeevi matrix is equivalent
to tightness of the underlying Gabor frame. For arbitrary oversampling, we furthermore consider tight Gabor frames canonically
associated to window functions g satisfying certain decay properties. Here, we show under what conditions and to what extent
the canonically associated tight frame inherits decay properties of g. Our proofs rely on the Zak transform, on the Zibulski-Zeevi
representation of the Gabor frame operator, on a result by Jaffard, on a functional calculus for Gabor frame operators, on
results from the theory of entire functions, and on the theory of polynomial matrices. 相似文献
5.
Under some assumptions on a function F and its Fourier transform
we prove new estimates of best approximation of F by entire functions of exponential type σ in Lp(
), 1 ≤ p < 2. The proof is based on some inequalities for
in L1(
) which may be treated as generalizations of results of Bausov and Telyakovskii. As an application we obtain exact estimates of best approximation of some infinitely differentiable functions. 相似文献
6.
David B. Nawrocki 《偏微分方程通讯》2013,38(9-10):1675-1734
Abstract The purpose of this note is to present an alternative proof of a result by H. Smith and C. Sogge showing that in odd dimension of space, local (in time) Strichartz estimates and exponential decay of the local energy for solutions to wave equations imply global Strichartz estimates. Our proof allows to extend the result to the case of even dimensions of space. 相似文献
7.
Jakob Lemvig 《Advances in Computational Mathematics》2009,30(3):231-247
For sufficiently small translation parameters, we prove that any bandlimited function ψ, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame with a dual frame
also having the wavelet structure. This dual frame is generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple construction procedure for pairs of dual wavelet frames whose
generators have compact support in the Fourier domain and desired time localization. The construction is based on characterizing
equations for dual wavelet frames and relies on a technical condition. We exhibit a general class of function satisfying this
condition; in particular, we construct piecewise polynomial functions satisfying the condition.
相似文献
8.
Carlo Blundo Sebastià Martín Barbara Masucci CarlEs Padró 《Designs, Codes and Cryptography》2004,33(3):241-260
A metering scheme is a method by which an audit agency is able to measure the interaction between servers and clients during a certain number of time frames. Naor and Pinkas (Vol. 1403 of LNCS, pp. 576–590) proposed metering schemes where any server is able to compute a proof (i.e., a value to be shown to the audit agency at the end of each time frame), if and only if it has been visited by a number of clients larger than or equal to some threshold h during the time frame. Masucci and Stinson (Vol. 1895 of LNCS, pp. 72–87) showed how to construct a metering scheme realizing any access structure, where the access structure is the family of all subsets of clients which enable a server to compute its proof. They also provided lower bounds on the communication complexity of metering schemes. In this paper we describe a linear algebraic approach to design metering schemes realizing any access structure. Namely, given any access structure, we present a method to construct a metering scheme realizing it from any linear secret sharing scheme with the same access structure. Besides, we prove some properties about the relationship between metering schemes and secret sharing schemes. These properties provide some new bounds on the information distributed to clients and servers in a metering scheme. According to these bounds, the optimality of the metering schemes obtained by our method relies upon the optimality of the linear secret sharing schemes for the given access structure. 相似文献
9.
In this article, the existence of a global strong solution for all finite time is derived for the Kirchhoff's model of parabolic type. Based on exponential weight function, some new regularity results which reflect the exponential decay property are obtained for the exact solution. For the related dynamics, the existence of a global attractor is shown to hold for the problem when the non-homogeneous forcing function is either independent of time or in L∞(L2). With the finite element Galerkin method applied in spatial direction keeping time variable continuous, a semidiscrete scheme is analyzed, and it is also established that the semidiscrete system has a global discrete attractor. Optimal error estimates in L∞(H1) norm are derived which are valid uniformly in time. Further, based on a backward Euler method, a completely discrete scheme is analyzed and error estimates are derived. It is also further, observed that in cases where f = 0 or f = O(e?γ0t) with γ0 > 0, the discrete solutions and error estimates decay exponentially in time. Finally, some numerical experiments are discussed which confirm our theoretical findings. 相似文献
10.
Refinable functions with exponential decay arise from applications such as the Butterworth filters in signal processing. Refinable
functions with exponential decay also play an important role in the study of Riesz bases of wavelets generated from multiresolution
analysis. A fundamental problem is whether the standard solution of a refinement equation with an exponentially decaying mask
has exponential decay. We investigate this fundamental problem by considering cascade algorithms in weighted L
p
spaces (1≤p≤∞). We give some sufficient conditions for the cascade algorithm associated with an exponentially decaying mask to converge
in weighted L
p
spaces. Consequently, we prove that the refinable functions associated with the Butterworth filters are continuous functions
with exponential decay. By analyzing spectral properties of the transition operator associated with an exponentially decaying
mask, we find a characterization for the corresponding refinable function to lie in weighted L
2 spaces. The general theory is applied to an interesting example of bivariate refinable functions with exponential decay,
which can be viewed as an extension of the Butterworth filters. 相似文献
11.
Perfectly matched layers in 1-d : energy decay for continuous and semi-discrete waves 总被引:2,自引:1,他引:1
In this paper we investigate the efficiency of the method of perfectly matched layers (PML) for the 1-d wave equation. The
PML method furnishes a way to compute solutions of the wave equation for exterior problems in a finite computational domain
by adding a damping term on the matched layer. In view of the properties of solutions in the whole free space, one expects
the energy of solutions obtained by the PML method to tend to zero as t → ∞, and the rate of decay can be understood as a measure of the efficiency of the method. We prove, indeed, that the exponential
decay holds and characterize the exponential decay rate in terms of the parameters and damping potentials entering in the
implementation of the PML method. We also consider a space semi-discrete numerical approximation scheme and we prove that,
due to the high frequency spurious numerical solutions, the decay rate fails to be uniform as the mesh size parameter h tends to zero. We show however that adding a numerical viscosity term allows us to recover the property of exponential decay
of the energy uniformly on h. Although our analysis is restricted to finite differences in 1-d, most of the methods and results apply to finite elements
on regular meshes and to multi-dimensional problems.
This work started while the first author was visiting the Department of Mathematics of the Universidad Autónoma de Madrid,
in the frame of the European program “New materials, adaptive systems and their nonlinearities: modeling, control and numerical
simulation” HPRN-CT-2002-00284. The work was finished while both authors visited the Isaac Newton Institute of Cambridge within
the Program “Highly Oscillatory Problems”. 相似文献
12.
We provide explicit constructions of particularly convenient dual pairs of Gabor frames. We prove that arbitrary polynomials
restricted to sufficiently large intervals will generate Gabor frames, at least for small modulation parameters. Unfortunately,
no similar function can generate a dual Gabor frame, but we prove that almost any such frame has a dual generated by a B-spline.
Finally, for frames generated by any compactly supported function φ whose integer-translates form a partition of unity, e.g., a B-spline, we construct a class of dual frame generators, formed
by linear combinations of translates of φ. This allows us to chose a dual generator with special properties, for example, the one with shortest support, or a symmetric
one in case the frame itself is generated by a symmetric function. One of these dual generators has the property of being
constant on the support of the frame generator. 相似文献
13.
An S-unimodal map f is said to satisfy the Collet-Eckmann condition if the lower Lyapunov exponent at the critical value is positive. If the
infimum of the Lyapunov exponent over all periodic points is positive then f is said to have a uniform hyperbolic structure. We prove that an S-unimodal map satisfies the Collet-Eckmann condition if
and only if it has a uniform hyperbolic structure. The equivalence of several non-uniform hyperbolicity conditions follows.
One consequence is that some renormalization of an S-unimodal map has an absolutely continuous invariant probability measure
with exponential decay of correlations if and only if the Collet-Eckmann condition is satisfied. The proof uses new universal
bounds that hold for any S-unimodal map without periodic attractors.
Oblatum 4-VII-1996 & 4-VII-1997 相似文献
14.
The exponential stability of singularly perturbed time-varying systems is investigated. It turns out that, under natural conditions, exponential stability of an averaged system is equivalent to exponential stability of the perturbed system for small perturbation parameters. Explicit estimates for both, the approximation of single trajectories and the order of the exponential decay, are obtained. The method of proof does not require smoothness of the averaged system. 相似文献
15.
Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-known that the system is exponentially stable if the kernel in the memory term is sub-exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions: What if the kernel is tested against a different function (say Gamma) other than the exponential function? Would there still be stability? In the affirmative, what kind of decay rate we get? It is proved that for a non-decreasing function “Gamma” whose “logarithmic derivative” is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential. 相似文献
16.
Shangkun Weng 《Mathematical Methods in the Applied Sciences》2016,39(15):4398-4418
In this paper, we first address the space‐time decay properties for higher‐order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proof is based on a parabolic interpolation inequality, bootstrap argument, and some weighted estimates. Secondly, we present a new solution integration formula for the Boussinesq system, which will be employed to establish the existence of strong solutions for small initial data in some scaling invariant function spaces. The smallness conditions are somehow weaker than those presented by Brandolese and Schonbek. We further investigate the asymptotic profiles and decay properties of these strong solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
Jaime Muñoz-Rivera 《Journal of Mathematical Analysis and Applications》2008,338(2):1296-1309
In this paper we investigate the temporal decay behavior of the solutions of the one-dimensional problem in various theories of continua with voids. It has been proved that the coupling of the elastic structure with porous microstructure is weak in the sense that in many situations the temporal decay of solutions is slow. We have considered some theories of porous continua when the deformation-rate tensor or time-rate or porosity function or thermal effects is present. We have proved that the decay cannot be controlled by a negative exponential. The natural question now is whether there exist or not a polynomial rate of decay of the solution in some appropriate norms. In this paper we consider some cases where the decay is slow and we obtain polynomial decay estimates. In concrete we consider the case when only the viscoelastic effect is present, the case when the motion of voids is assumed to be quasi-static and the porous viscosity is present and we finish with the case of the porous-elasticity when thermal effect is coupled. 相似文献
18.
The model of zero-knowledge multi-prover interactive proofs was introduced by Ben-Or, Goldwasser, Kilian and Wigderson in [4]. A major open problem associated with this model is whether NP problems can be proven by one-round, two-prover, zero-knowledge protocols with exponentially small error probability (e.g. via parallel executions). A positive answer was claimed by Fortnow, Rompel and Sipser in [12], but its proof was later shown to be flawed by Fortnow who demonstrated that the probability of cheating inn independent parallel rounds can be much higher than the probability of cheating inn independent sequential rounds (with exponential ratio between them). In this paper we solve this problem: We show a new one-round two-prover interactive proof for Graph Hamiltonicity, we prove that it is complete, sound and perfect zeroknowledge, and thus every problem in NP has a one-round two-prover interactive proof which is perfectly zero knowledge under no cryptographic assumptions. The main difficulty is in proving the soundness of our parallel protocol namely, proving that the probability of cheating in this one-round protocol is upper bounded by some exponentially low threshold. We prove that this probability is at most 1/2
n/9 (wheren is the number of parallel rounds), by translating the soundness problem into some extremal combinatorial problem, and then solving this new problem. 相似文献
19.
Using a variational principle for s-numbers, we obtain estimates for the linear, Gel′fand. and Bernstein n-widths. A simple proof of some results concerned with the exact values of n-widths of diagonal operators is given. We also calculate the exact values at the Bernstein n-widths for the Hardy-Sobolev classes. 相似文献
20.
The two-body S-matrix for an interaction with exponential decay at infinity is defined in a time-independent way and its unitarity is proved directly by local distortion techniques. Complete sets of incoming and outgoing states, or delicate resolvent estimates are not needed for the proof. 相似文献