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1.
On the jump behavior of distributions and logarithmic averages 总被引:1,自引:0,他引:1
Jasson Vindas Ricardo Estrada 《Journal of Mathematical Analysis and Applications》2008,347(2):597-606
The jump behavior and symmetric jump behavior of distributions are studied. We give several formulas for the jump of distributions in terms of logarithmic averages, this is done in terms of Cesàro-logarithmic means of decompositions of the Fourier transform and in terms of logarithmic radial and angular local asymptotic behaviors of harmonic conjugate functions. Application to Fourier series are analyzed. In particular, we give formulas for jumps of periodic distributions in terms of Cesàro–Riesz logarithmic means and Abel–Poisson logarithmic means of conjugate Fourier series. 相似文献
2.
George K. Yang 《Applicable analysis》2013,92(5):501-507
We investigate the wavelet transforms of tempered distributions in a way that closely links their Fourier transforms and wavelet transforms. Two exchange formulas of the convolution and the multiplication of wavelet transforms of tempered distributions are established. We call these formulas the quasi-exchange formulas for wavelet transforms of distributions, because of the resemblance between these formulas and the well-known exchange formula for Fourier transforms. 相似文献
3.
Yongsheng Han Shanzhen Lu Dachun Yang 《Journal of Fourier Analysis and Applications》2001,7(6):571-600
In this article a Littlewood-Paley theorem for a new kind of Littlewood-Paley g-functions over spaces of homogeneous type
is presented. Based on it the authors establish inhomogeneous discrete Calderón reproducing formulas for spaces of homogeneous
type, making use of Calderón-Zygmund operators. 相似文献
4.
Nicholas J. Daras 《Numerical Algorithms》1999,20(4):285-301
Padé-type approximation is the rational function analogue of Taylor’s polynomial approximation to a power series. A general
method for obtaining Padé-type approximants to Fourier series expansions of harmonic functions is defined. This method is
based on the Newton-Cotes and Gauss quadrature formulas. Several concrete examples are given and the convergence behavior
of a sequence of such approximants is studied.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Serge Dubuc Daniel Lemire Jean-Louis Merrien 《Journal of Fourier Analysis and Applications》2001,7(5):537-552
Two subdivision schemes with Hermite data on ℤ are studied. These schemes use 2 or 7 parameters respectively depending on
whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameter space,
the schemes are convergent in the space of Schwartz distributions. The Fourier transform of any interpolating function can
be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional
equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come
from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support
and a theorem of Artzrouni about convergent products of matrices. 相似文献
6.
Jean-Louis Clerc 《Journal of Fourier Analysis and Applications》2000,6(1):105-111
The classical Hecke identity gives the Fourier transform of the product of a homogeneous harmonic polynomial h times the Gaussian
e−1/2<...>. A similar formula is valid when the Gaussian is replaced by the tempered distribution ei/2<...>. It is shown that there is a similar identity when the inner product is replaced by an indefinite quadratic formq and h is a Л-harmonic distribution, where Л is the differential operator canonically associated toq. Another generalization is obtained in the context of representations of Jordan algebras, in the spirit of Herz's previous
work on matrix spaces. 相似文献
7.
We study the Jordan structures and geometry of bounded matrix-valued harmonic functions on a homogeneous space and their analogue, the harmonic functionals, in the setting of Fourier algebras of homogeneous spaces.Supported by EPSRC grant GR/G91182 and NSERC grant 7679. 相似文献
8.
F. Móricz 《Archiv der Mathematik》2003,81(1):82-89
We extend the concept of and basic results on statistical convergence from
ordinary (single) sequences to multiple sequences of (real or complex) numbers.
As an application to Fourier analysis, we obtain the following Theorem 3: (i)
If $f \in L(\textrm{log}^{+} L)^{d-1}(\mathbb{T}^d)$, where $\mathbb{T}^d := [-\pi, \pi)^{d}$
is the d-dimensional torus, then the Fourier
series of f is statistically convergent to $f({\bf t})$
at almost every ${\bf t} \in \mathbb{T}^d$; (ii) If $f \in C(\mathbb{T}^d)$, then the
Fourier series of f
is statistically convergent to $f ({\bf t})$ uniformly on $\mathbb{T}^d$.
Received: 5 November 2001 相似文献
9.
Mirjana Stojanovi? 《Journal of Computational and Applied Mathematics》2011,235(10):3121-3137
We find solutions for the diffusion-wave problem in 1D with n-term time fractional derivatives whose orders belong to the intervals (0,1),(1,2) and (0,2) respectively, using the method of the approximation of the convolution by Laguerre polynomials in the space of tempered distributions. This method transfers the diffusion-wave problem into the corresponding infinite system of linear algebraic equations through the coefficients, which are uniquely solvable under some relations between the coefficients with index zero.The method is applicable for nonlinear problems too. 相似文献
10.
Herbert H.H. Homeier 《Numerical Algorithms》1998,18(1):1-30
We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain
Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that
this sequence transformation is a special case of the J transformation. Thus, many properties of the I transformation can
be deduced from the known properties of the J transformation (like the kernel, determinantal representations, and theorems
on convergence behavior and stability). Besides explicit formulas for the kernel, some basic convergence theorems for the
I transformation are given here. Further, numerical results are presented that show that suitable variants of the I transformation
are powerful nonlinear convergence accelerators for Fourier series with coefficients of monotonic behavior.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
11.
Anry Nersessian 《Numerical Functional Analysis & Optimization》2013,34(1-2):227-240
The general scheme, suggested in [1] using a basis of an infinite-dimensional space and allowing to construct finite-dimensional orthogonal systems and interpolation formulas, is improved in the paper. This results particularly in a generalization of the well-known scheme by which periodic interpolatory wavelets are constructed. A number of systems which do not satisfy all the conditions for multiresolution analysis but have some useful properties are introduced and investigated. Starting with general constructions in Hilbert spaces, we give a more careful consideration to the case connected with the classic Fourier basis. Convergence of expansions which are similar to partial sums of the summation method of Fourier series, as well as convergence of interpolation formulas are considered. Some applications to fast calculation of Fourier coefficients and to solution of integrodifferential equations are given. The corresponding numerical results have been obtained by means of MATHEMATICA 3.0 system. 相似文献
12.
We show that, given a tempered distribution S whose Fourier transform is a function of polynomial growth, a point x in
is outside the support of S if and only if the Fourier integral of S is summable in Bochner-Riesz means to zero uniformly on a neighbourhood of x.
Received: 29 December 2005 相似文献
13.
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
14.
We show by example that the classical characterization of the Fourier series of periodic functions in Lp, 1<p≤+∞, as those trigonometric series whose Abel or Fejér means are uniformly bounded in Lp does not hold for general (non-periodic) trigonometric series in relation to Stepanov-almost-periodic functions, but that
it does hold under the additional hypothesis that the means are translation equicontinuous. We exhibit a bounded, infinitely
differentiable function that belongs to every class of Besicovitch-almost-periodic functions but is not equivalent in the
metric of Besicovitch-almost-periodic functions to any Stepanov-almost-periodic function. 相似文献
15.
George K. Yang 《Applicable analysis》2013,92(5):1019-1032
We study the wavelet transforms of tempered distributions via unitary irreducible representations, Fourier transforms, and the wavelet transforms of infinitely differentiable functions of rapid descent. We explore the general properties, and derive the pseudo-exchange formulas for wavelet transforms of tempered distributions. While the new formulas are rather different from the exchange formula for Fourier transforms of distributions, yet the pseudo-exchange formulas still exchange the products of convolution and the products of multiplication of tempered distributions. 相似文献
16.
Pedro Catuogno Christian Olivera 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):479-493
In this work we introduce an algebra of tempered generalized functions. The tempered distributions are embedded in this algebra via their Hermite expansions. The Fourier transform is naturally extended to this algebra in such a way that the usual relations involving multiplication, convolution and differentiation are valid. Furthermore, we give a generalized Itô formula in this context and some applications to stochastic analysis. 相似文献
17.
Ferenc Móricz 《Journal of Fourier Analysis and Applications》2001,7(6):601-614
A theorem of Fejér states that if a periodic function F is of bounded variation on the closed interval [0, 2π], then the nth
partial sum of its formally differentiated Fourier series divided by n converges to π-1[F(x+0)-F(x-0)] at each point x. The generalization of this theorem for Fourier-Stieltjes series of (nonperiodic) functions of bounded variation
is also well known.
The aim of the present article is to extend these results to the (m, n)th rectangular partial sum of double Fourier or Fourier-Stieltjes
series of a function F(x, y) of bounded variation over the closed square [0, 2π]×[0, 2π] in the sense of Hardy and Krause.
As corollaries, we also obtain the following results:
相似文献
(i) | The terms of the Fourier or Fourier-Stieltjes series of F(x, y) determine the atoms of the (periodic) Borel measure induced by (an appropriate extension of) F. |
(ii) | In the case of periodic functions F(x, y) of bounded variation, the class of double Fourier-Stieltjes series coincides with the class of series that can be obtained from their Fourier series by a formal termwise differentiation with respect to both x and y. |
18.
Stable laws can be tempered by modifying the Lévy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena. 相似文献
19.
The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential
of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more
general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the
roots, we obtain characterizations of the subderivative and regular subdifferential for these functions as well. In particular,
we completely characterize the subderivative and regular subdifferential of the radius mapping (the maximum of the moduli
of the roots). The abscissa and radius mappings are important for the study of continuous and discrete time linear dynamical
systems.
Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday. Terry is one of those rare individuals who combine
a broad vision, deep insight, and the outstanding writing and lecturing skills crucial for engaging others in his subject.
With these qualities he has won universal respect as a founding father of our discipline. We, and the broader mathematical
community, owe Terry a great deal. But most of all we are personally thankful to Terry for his friendship and guidance.
Research supported in part by the National Science Foundation Grant DMS-0203175.
Research supported in part by the Natural Sciences and Engineering Research Council of Canada.
Research supported in part by the National Science Foundation Grant DMS-0412049. 相似文献
20.
Jacob Steinberg 《Acta Appl Math》1985,3(2):115-133
It is shown that a well-known series expansion of the stress function around a tip of a crack in an elastic plate, converges on a two-sheet Riemann surface. Explicit expressions for its coefficients, the stress intensity factors, are obtained. More generally, a new series expansion around the whole crack is found and investigated. 相似文献