共查询到20条相似文献,搜索用时 0 毫秒
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The order of magnitude of multiple Fourier coefficients of complex valued functions of generalized bounded variations like (Λ1 , ,ΛN )BV(p) and r-BV, over [0,2π]N , are estimated. 相似文献
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Z. Németh 《Acta Mathematica Hungarica》2000,88(4):347-357
In a recent paper [1], Bagota, Giang, and Móricz investigated the order of magnitude of Fourier transform, in (C, ) sensse. We generalize these results to more general integral transforms. 相似文献
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Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
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Susana Elena Trione 《Studies in Applied Mathematics》1976,55(4):315-326
We extend the distributional Bochner formula [1, p. 72, Theorem 26] to certain kinds of distributions. Theorem I.1 gives a formula [Eq. (I.1.14)] which makes it possible to obtain easily the Fourier transform of distributions of the form As applications of the formula (I.1.14) we evaluate the Fourier transforms of the distributions Gα(P±i0, m, n) [Eq. (I.4.1)] and Hα(P±i0,n) [Eq. (II.1.1)]. It follows from Theorem II.3 that Hzk(P±i0,n) is, for 2K≠n+2r, r=0,1..., an elementary solution of the n-dimensional ultrahyperbolic operator iterated k times. 相似文献
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S Winograd 《Advances in Mathematics》1979,32(2):83-117
Most results in multiplicative complexity assume that the functions to be computed are in the field of constants extended by indeterminates, that is, the variables satisfy no algebraic relation. In this paper we extend some of the known results to the case that some of the variables do satisfy some algebraic relations. We then apply these results to obtaining a lower bound on the multiplicative complexity of the Discrete Fourier Transform. In the special case of computing the Discrete Fourier Transform of a prime number of points, the lower bound is actually attainable. 相似文献
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《Applied and Computational Harmonic Analysis》2001,10(1):45-60
We present the windowed Fourier transform and wavelet transform as tools for analyzing persistent signals, such as bounded power signals and almost periodic functions. We establish the analogous Parseval-type identities. We consider discretized versions of these transforms and construct generalized frame decompositions. Finally, we bring out some relations with shift-invariant operators and linear systems. 相似文献
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本文引入了一种新的广义级来研究由二重Laplace-Stieltjes变换所定义的全纯函数的增长性, 并建立了一些最大模与最大项之间的有趣的关系,推广了Laplace-Stieltjes变换的某些结果. 相似文献
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The fast Fourier transform can be used to invert z transforms(including probability generating functions), but this applicationhas received little attention or use. This correspondence makesa case for the FFT as a standard numerical tool in queuing andother statistical analyses in order to obtain probability densityfunctions quickly and easily. Round-off and aliasing errorsare discussed briefly for the queuing analyst without a signalprocessing background. Several variations are described whichextend the accuracy and the utility of the method. 相似文献
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Let SL(2, R) be the group of all real matrices of order 2 with determinant 1. In this paper, weuse G to denote both SL(2, R) and the lie group SU(1,1) = {(α/ββ/α):|α|2-|β|2=1,α,β∈C}because they are isomorphic to each other[1]. 相似文献
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本文针对小波变换教学中小流变换概念理解困难的问题,提出了一种比较教学方法,通过分析小波变换与傅立叶变换之间的联系,并从四个方面进行对比,清楚地描述了小波变换的本质,从而对加深对小波变换的理解。 相似文献
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In this paper, the theory of the spinor Fourier transform introduced in [Batard T, Berthier M, Saint-Jean C, Clifford-Fourier Transform for Color Image Processing, Geometric Algebra Computing for Engineering and Computer Science (E. Bayro-Corrochano and G. Scheuermann Eds.), Springer, London, 2010, pp. 135–161] is further developed. While in the original paper, the transform was determined for vector-valued functions only, it now will be extended to functions taking values in the entire Clifford algebra. Next, two bases are determined under which this Fourier transform is diagonalizable. A main stumbling block for further applications, in particular concerning filter design in the Fourier domain, is the lack of a proper convolution theorem. This problem will be tackled in the final section of this paper. 相似文献
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Mathematical Notes - It is well known that the classical and Sobolev wave fronts were extended to nonequivalent global versions by the use of the short-time Fourier transform. In this very short... 相似文献
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In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained. 相似文献
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An approach to the inversion formula for the Fourier transform is proposed in some special case of characteristic functions. Bibliography: 6 titles. 相似文献
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Ferenc Weisz 《Integral Equations and Operator Theory》2008,60(1):133-149
So-called short-time Fourier transform multipliers (also called Anti-Wick operators in the literature) arise by applying a
pointwise multiplication operator to the STFT before applying the inverse STFT. Boundedness results are investigated for such
operators on modulation spaces and on L
p
-spaces. Because the proofs apply naturally to Wiener amalgam spaces the results are formulated in this context. Furthermore,
a version of the Hardy-Littlewood inequality for the STFT is derived.
This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship
No M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No K67642. 相似文献
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We study relative Fourier–Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew–commutativity relation between this equivalence of categories and certain duality functors. We use our results to explicitly construct examples of semi-stable sheaves on degenerating families of elliptic curves. 相似文献