共查询到20条相似文献,搜索用时 31 毫秒
1.
Hask?z Co?kun 《Journal of Mathematical Analysis and Applications》2002,276(2):833-844
We consider Hill's equation y″+(λ−q)y=0 where q∈L1[0,π]. We show that if ln—the length of the n-th instability interval—is of order O(n−(k+2)) then the real Fourier coefficients ank,bnk of q(k)—k-th derivative of q—are of order O(n−2), which implies that q(k) is absolutely continuous almost everywhere for k=0,1,2,…. 相似文献
2.
Wojciech Czaja 《Journal of Mathematical Analysis and Applications》2003,284(1):389-396
We study classes of pseudodifferential operators which are bounded on large collections of modulation spaces. The conditions on the operators are stated in terms of the Lp,q estimates for the continuous Gabor transforms of their symbols. In particular, we show how these classes are related to the class of operators of Gröchenig and Heil, which is bounded on all modulation spaces. 相似文献
3.
For a function f:{0,1}n→R and an invertible linear transformation L∈GLn(2), we consider the function Lf:{0,1}n→R defined by Lf(x)=f(Lx). We raise two conjectures: First, we conjecture that if f is Boolean and monotone then I(Lf)≥I(f), where I(f) is the total influence of f. Second, we conjecture that if both f and L(f) are monotone, then f=L(f) (up to a permutation of the coordinates). We prove the second conjecture in the case where L is upper triangular. 相似文献
4.
Jan Vybíral 《Journal of Functional Analysis》2011,260(4):1096-1105
We continue our study of the Johnson-Lindenstrauss lemma and its connection to circulant matrices started in Hinrichs and Vybíral (in press) [7]. We reduce the bound on k from k=Ω(ε−2log3n) proven there to k=Ω(ε−2log2n). Our technique differs essentially from the one used in Hinrichs and Vybíral (in press) [7]. We employ the discrete Fourier transform and singular value decomposition to deal with the dependency caused by the circulant structure. 相似文献
5.
We give an example of a Gaussian random Fourier series, of which the normalized remainders have their sojourn times converging in variation, namely the convergence in the space L1(R) of the related density distributions, to the Gaussian density. The convergence in the space L∞(R) is also proved. In our approach, we use local times of Gaussian random Fourier series. 相似文献
6.
In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems: for any ε∈(0, 1), there exists a measurable set E [0, 1)of measure bigger than 1-ε such that for any function f ∈ L~1[0, 1), it is possible to find a function g ∈ L~1[0, 1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing. 相似文献
7.
Carmen Fernández 《Advances in Mathematics》2010,224(5):1904-1926
We obtain a class of subsets of R2d such that the support of the short time Fourier transform (STFT) of a signal f∈L2(Rd) with respect to a window g∈L2(Rd) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L2-norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces. 相似文献
8.
《Applied Mathematical Modelling》2014,38(21-22):5126-5148
This article applies the golden section search method (GSSM), simplex search method (SSM) and differential evolution (DE) for predicting the unknown Fourier number (Fo), Vernotte number (Ve) and non-dimensional solar heat flux (S1) in a flat-plate solar collector when subjected to a given temperature requirement. The required temperature field is calculated using an analytical forward method by considering Fourier and non-Fourier heat conduction, and using this, the inverse problem is solved to predict the Fo, Ve and S1 which are assumed to be the unknown parameters. The study reveals that the temperature field is highly sensitive to the Fo, thus even a small error in the temperature measurement can result in an unrealistic estimation of heating time of the collector. The present study is proposed to be useful in determining the time, the time lag and solar heat flux for controlled heating of an absorber plate within a stipulated time, which will be required to attain a prescribed/desired temperature distribution. Additionally, the study also shows that subjected to different time levels, the same temperature distribution is possible through different absorber plate materials. It has been observed from the present study that apart from SSM and DE, GSSM fails to estimate the unknown parameters at large value of Ve and small value of Fo, due to the associated fluctuation in the measured temperature field. The present study further discusses the computational performance of direct search method (e.g. GSSM and SSM) with that of the evolutionary method (DE) in terms of the maximum number of iteration and CPU time required to achieve the desired objective. 相似文献
9.
Huixue LAO 《数学年刊B辑(英文版)》2012,33(6):877-888
Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full modular group. Let ?? f (n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2 f, s) is the symmetric square L-function associated with f(z), and $ \lambda _{sym^2 f} (n) $ (n) denotes the nth coefficient L(sym2 f, s). In this paper, it is proved that $$ \sum\limits_{n \leqslant x} {\lambda _{sym^2 f}^4 (n)} = xP2(\log x) + O(x^{\frac{{79}} {{81}} + \varepsilon } ), $$ , where P 2(t) is a polynomial in t of degree 2. Similarly, it is obtained that $$ \sum\limits_{n \leqslant x} {\lambda _f^4 (n^2 )} = x\tilde P2(\log x) + O(x^{\frac{{79}} {{81}} + \varepsilon } ), $$ , where $ \tilde P_2 (t) $ is a polynomial in t of degree 2. 相似文献
10.
In this paper, we consider a class of Fourier multipliers whose symbols are controlled by a polynomial on starlike Lipschitz surfaces and get the L2 boundedness of these operators on Sobolev spaces and their endpoint estimates. 相似文献
11.
Chun-Kit Lai 《Journal of Functional Analysis》2011,261(10):2877-2889
Let μ be a compactly supported absolutely continuous probability measure on Rn, we show that L2(K,dμ) admits a Fourier frame if and only if its Radon-Nikodym derivative is bounded above and below almost everywhere on the support K. As a consequence, we prove that if μ is an equal weight absolutely continuous self-similar measure on R1 and L2(K,dμ) admits a Fourier frame, then the density of μ must be a characteristic function of self-similar tile. In particular, this shows for almost everywhere 1/2<λ<1, the L2 space of the λ-Bernoulli convolutions cannot admit a Fourier frame. 相似文献
12.
V. A. Abilov F. V. Abilova M. K. Kerimov 《Computational Mathematics and Mathematical Physics》2008,48(12):2146-2153
For the Fourier transform in the space L 2(?2) of square integrable multivariable functions, two practically useful estimates are proved in certain classes of functions characterized by a generalized continuity modulus. 相似文献
13.
Let G be a compact nonmetrizable topological group whose local weight b(G) has uncountable cofinality. Let H be an amenable locally compact group, A(G×H) the Fourier algebra of G×H, and UC2(G×H) the space of uniformly continuous functionals in VN(G×H)=A∗(G×H). We use weak factorization of operators in the group von Neumann algebra VN(G×H) to prove that there exist at least 2b(G)2 left ideals of dimensions at least 2b(G)2 in A(G×H)∗∗ and in UC2∗(G×H). We show that every nontrivial right ideal in A(G×H)∗∗ and in UC2∗(G×H) has dimension at least 2b(G)2. 相似文献
14.
A well-known result for Vilenkin systems is the fact that for all 1 p ∞ the n-th partial sums of Fourier series of all functions in the space Lpconverge to the function in Lp-norm.This statement can not be generalized to any representative product system on the complete product of finite non-abelian groups,but even then it is true for the complete product of quaternion groups with bounded orders and monomial representative product system ordered in a specific way. 相似文献
15.
LIU Feng WU Huo-xiong 《高校应用数学学报(英文版)》2014,29(1):86-100
In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ 1 and the sphere function Ω∈ Fβ(Sn.1) for some β 0,which is distinct from H1(Sn.1). 相似文献
16.
17.
Vladimir Varlamov 《Journal of Mathematical Analysis and Applications》2010,370(2):687-1648
A new integral representation of the Hankel transform type is deduced for the function Fn(x,Z)=Zn−1Ai(x−Z)Ai(x+Z) with x∈R, Z>0 and n∈N. This formula involves the product of Airy functions, their derivatives and Bessel functions. The presence of the latter allows one to perform various transformations with respect to Z and obtain new integral formulae of the type of the Mellin transform, K-transform, Laplace and Fourier transform. Some integrals containing Airy functions, their derivatives and Chebyshev polynomials of the first and second kind are computed explicitly. A new representation is given for the function 2|Ai(z)| with z∈C. 相似文献
18.
César J. Niche Gabriela Planas 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(1):244-256
We consider the Navier-Stokes equations with delays in Rn,2≤n≤4. We prove existence of weak solutions when the external forces contain some hereditary characteristics and uniqueness when n=2. Moreover, if the external forces satisfy a time decay condition we show that the solution decays at an algebraic rate. 相似文献
19.
It is well-known that if an one-dimensional function is continuously differentiable on [0, 1], then its Fourier-Haar series converges absolutely. On the other hand, if a function of two variables has continuous partial derivatives f x ′ and f y ′ on T 2, then its Fourier series does not necessarily absolutely converge with respect to a multiple Haar system (see [1]). In this paper we state sufficient conditions for the absolute convergence of the Fourier-Haar series for two-dimensional continuously differentiable functions. 相似文献
20.
Hartmut Pecher 《Journal of Mathematical Analysis and Applications》2008,342(2):1440-1454
The 1D Cauchy problem for the Zakharov system is shown to be locally well-posed for low regularity Schrödinger data and wave data under certain assumptions on the parameters k,l and 1<p?2, where , generalizing the results for p=2 by Ginibre, Tsutsumi and Velo. Especially we are able to improve the results from the scaling point of view, and also allow suitable k<0, l<−1/2, i.e. data u0∉L2 and (n0,n1)∉H−1/2×H−3/2, which was excluded in the case p=2. 相似文献