共查询到20条相似文献,搜索用时 7 毫秒
1.
We show that,given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value τ(in the sense of Lojasiewicz),the Fourier integral of T at x is summable in Bochner-Riesz means to τ. 相似文献
2.
Michael Taylor 《Journal of Fourier Analysis and Applications》1999,5(5):449-463
We prove a number of results about pointwise convergence of eigenfunction expansions of functions on compact manifolds. In particular, we establish that the Pinsky phenomenon holds for piecewise smooth functions on the three-dimensional torus, with jump across the boundary of a ball, in the same form as it was discovered for functions on three-dimensional Euclidean space. Our work on this has been stimulated by recent work of Brandolini and Colzani, and we also discuss some variants of their results. 相似文献
3.
Michael E. Taylor 《Proceedings of the American Mathematical Society》2001,129(7):2001-2003
In this note we complete a circle of results presented in §5 of an earlier work of the author (J. Fourier Anal. 5 (1999), 449-463), establishing the endpoint case of Proposition 10 of that paper. As a consequence, we have results on pointwise convergence of the Fourier series (summed by spheres) of a function on the 3-dimensional torus with a simple jump across a smooth surface , with no curvature hypotheses on , extending Proposition 7 of that paper.
4.
Research was completed while the second named author was a visiting professor at the University of the Witwatersrand, Republic of South Africa, during the spring semester in 1992. 相似文献
5.
The problem of studying the largest rearrangement invariantspace of functions with almost everywhere convergent Fourierseries is considered. A quasi-Banach space QA of functions isdefined with almost everywhere convergent Fourier series thatstrictly contains Antonov and Soria's spaces (L log L log loglog L and ). 相似文献
6.
We prove a vector-valued version of Carleson’s theorem: let $Y=[X,H]_\theta $ be a complex interpolation space between an unconditionality of martingale differences (UMD) space $X$ and a Hilbert space $H$ . For $p\in (1,\infty )$ and $f\in L^p(\mathbb T ;Y)$ , the partial sums of the Fourier series of $f$ converge to $f$ pointwise almost everywhere. Apparently, all known examples of UMD spaces are of this intermediate form $Y=[X,H]_\theta $ . In particular, we answer affirmatively a question of Rubio de Francia on the pointwise convergence of Fourier series of Schatten class valued functions. 相似文献
7.
8.
Journal of Fourier Analysis and Applications - 相似文献
9.
Mark A. Pinsky 《纯数学与应用数学通讯》1994,47(5):653-681
Necessary and sufficient conditions are found for the convergence at a pre-assigned point of the spherical partial sums (resp. integrals) of the Fourier series (resp. integral) in the class of piecewise smooth functions on Euclidean space. These results carry over unchanged to spherical harmonic expansions, Fourier transforms on hyperbolic space, and Dirichlet eigenfunction expansions with respect to the Laplace operator on a class of Riemannian manifolds. © 1994 John Wiley & Sons, Inc. 相似文献
10.
S. Jaffard 《Applied and Computational Harmonic Analysis》2010,28(3):251-266
We investigate how the regularity of nonharmonic Fourier series is related to the spacing of their frequencies. This is obtained by using a transform which simultaneously captures the advantages of the Gabor and wavelet transforms. Applications to the everywhere irregularity of solutions of some PDEs are given. We extend these results to the anisotropic setting in order to derive directional irregularity criteria. 相似文献
11.
《Journal of Computational and Applied Mathematics》2006,196(2):540-552
The classical smoothing data problem is analyzed in a Sobolev space under the assumption of white noise. A Fourier series method based on regularization endowed with generalized cross validation is considered to approximate the unknown function. This approximation is globally optimal, i.e., the mean integrated squared error reaches the optimal rate in the minimax sense. In this paper the pointwise convergence property is studied. Specifically, it is proved that the smoothed solution is locally convergent but not locally optimal. Examples of functions for which the approximation is subefficient are given. It is shown that optimality and superefficiency are possible when restricting to more regular subspaces of the Sobolev space. 相似文献
12.
Functions of the Laplace operator F(− Δ) can be synthesized from the solution operator to the wave equation. When F is the characteristic function of [0, R
2
], this gives a representation for radial Fourier inversion. A number of topics related to pointwise convergence or divergence
of such inversion, as R → ∞, are studied in this article. In some cases, including analysis on Euclidean space, sphers, hyperbolic
space, and certain other symmetric spaces, exact formulas for fundamental solutions to wave equations are available. In other
cases, parametrices and other tools of microlocal analysis are effective. 相似文献
13.
W. Łenski 《Acta Mathematica Hungarica》2007,115(3):215-233
We present an estimation of the
and H
u
λφ
f means as approximation versions of the Totik type generalization (see [6, 7]) of the result of G. H. Hardy, J. E. Littlewood,
considered by N. L. Pachulia in [5]. Some results on the norm approximation will also be given.
相似文献
14.
Conditions for pointwise Fourier inversion using spherical Cesàromeans of a given degree are established on rank 1 noncompactsymmetric spaces. 相似文献
15.
16.
, . , L
p
(2) p>1 . , C(T3), - , . - .
This work was completed while the first named author was a visiting professor at Indiana University, Bloomington, Indiana; and the second named author was a visiting professor at Ohio State University, Columbus, Ohio, U.S.A. 相似文献
This work was completed while the first named author was a visiting professor at Indiana University, Bloomington, Indiana; and the second named author was a visiting professor at Ohio State University, Columbus, Ohio, U.S.A. 相似文献
17.
Alcides Buss 《Bulletin of the Brazilian Mathematical Society》2008,39(4):555-571
In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel
weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier inversion
Theorem for strictly-unconditionally integrable Fourier transforms. Our results generalize and improve those previously obtained
by Ruy Exel in the case of Abelian groups.
Supported by CAPES, Brazil. 相似文献
18.
Ferenc Móricz 《Monatshefte für Mathematik》2006,61(4):51-59
We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions
of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries,
we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and
a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version. 相似文献
19.
Ferenc Móricz 《Monatshefte für Mathematik》2006,148(1):51-59
We extend some recent results of S. A. Telyakovskii on the uniform boundedness of the partial sums of Fourier series of functions
of bounded variation to periodic functions of two variables, which are of bounded variation in the sense of Hardy. As corollaries,
we obtain the classical Parseval formula, the convergence theorem of the series involving the sine Fourier coefficients, and
a lower estimate of the best approximation by trigonometric polynomials in the metric of L in a sharpened version.
This research was supported by the Hungarian National Foundation for Scientific Research under Grants TS 044 782 and T 046
192. 相似文献
20.
Mark A. Pinsky 《Journal of Theoretical Probability》1993,6(1):187-193
A density functionf(x),xR
n
is said to bepiecewise smooth if for eachxR
n
, the mean value function
is piecewiseC
with compact support. (d is normalized surface measure on the unit sphere). The Fourier transform is
with spherical partial sum
.
Theorem. For suchf, lim
r
f
R
(x)=M
0+f(x) if and only ifrM
r
f(x) hask=[(n–3)/2] continuous derivatives. ([]=integer part). Otherwise we have lim
where 0 is uniquely determined. 相似文献