共查询到20条相似文献,搜索用时 375 毫秒
1.
A.J.E.M. Janssen 《Journal of Fourier Analysis and Applications》2005,11(5):577-588
For
let
be the set of all
for which
, where
is the orthonormal base of Hermite functions. We show that
if and only if
and that
if and only if
. Here S0 is Feichtinger’s space. 相似文献
2.
Alexander M. Powell 《Journal of Fourier Analysis and Applications》2005,11(4):375-387
We show that there exists an orthonormal basis
for
such that
and
are bounded
sequences. We also show that there does not exist any orthonormal basis
for
,
and
being bounded sequences.
This is motivated by a question posed by H.S. Shapiro on the mean and variance
sequences associated to orthonormal bases. 相似文献
3.
In this article we obtain the boundedness of the periodic, discrete and ergodic
bilinear Hilbert transform, from
,
where
1$, and $p_3\ge 1$" align="middle" border="0">
. The main techniques are a bilinear version of the transference method of Coifman and Weiss and certain discretization of bilinear operators. In the periodic case, we also obtain the boundedness for
相似文献
4.
Z. Ditzian 《Journal of Fourier Analysis and Applications》2005,11(4):489-496
For the Fejer means on
an equivalence between the rate of its convergence and an appropriate
K-functional is established. For the Bochner-Riesz means on
an equivalence between the rate of convergence and the corresponding K-functional is obtained. The results are of the form of strong converse inequality of type A. 相似文献
5.
Given a positive locally finite Borel measure μ on R, a natural way to construct
multifractal wavelet series
is to set
, where
. Indeed, under suitable conditions,
it is shown that the function Fμ inherits the multifractal properties of μ.
The transposition of multifractal properties works with many classes of statistically selfsimilar
multifractal measures, enlarging the class of processes which have self-similarity properties
and controlled multifractal behaviors. Several perturbations of the wavelet coefficients and their impact on the multifractal
nature
of Fμ are studied. As an application, multifractal Gaussian processes associated with Fμ are
created. We obtain results for the multifractal spectrum of the so-called W-cascades introduced
by Arnéodo et al. 相似文献
6.
An affine pseudo-plane X is a smooth affine surface defined over
which is endowed with an
-fibration such that every fiber is irreducible and only one fiber is a multiple fiber. If there is a hyperbolic
-action on X and X is an
-surface, we shall show that the universal covering
is isomorphic to an affine hypersurface
in the affine 3-space
and X is the quotient of
by the cyclic group
via the action
where
and
It is also shown that a
-homology plane X with
and a nontrivial
-action is an affine pseudo-plane. The automorphism group
is determined in the last section. 相似文献
7.
D.S. Lubinsky 《Constructive Approximation》2007,25(3):303-366
Assume
is not an integer. In papers published in 1913 and 1938,
S.~N.~Bernstein established the limit
Here
denotes the error in best uniform approximation of
by polynomials
of degree
. Bernstein proved that
is itself the error in best uniform approximation of
by entire functions of exponential type at most 1,
on the whole real line. We prove that the best approximating entire function
is unique, and satisfies an alternation property. We show that the scaled
polynomials of best approximation converge to this unique entire function.
We derive a representation for
, as well
as its
analogue for
. 相似文献
8.
Maria Roginskaya Michal Wojciechowski 《Journal of Fourier Analysis and Applications》2006,12(2):213-223
We study how the singularity (in the sense of Hausdorff dimension) of a vector valued measure can be affected by certain restrictions
imposed on its Fourier transform. The restrictions, we are interested in, concern the direction of the (vector) values of
the Fourier transform. The results obtained could be considered as a generalizations of F. and M. Riesz theorem, however a
phenomenon,
which have no analogy in the scalar case, arise in the vector valued case. As an example of application, we show that every
measure from
annihilating gradients
of
embedded in the natural way into
i.e., such that
for
, has Hausdorff dimension at least one. We provide examples which show both completeness and incompleteness of our results. 相似文献
9.
Denote by
the real-linear span of
, where
Under the concept of left-monogeneity defined through the generalized
Cauchy-Riemann operator we obtain the direct sum decomposition of
where
is the right-Clifford module of finite linear combinations of functions of the form
, where, for
, the function R is a k- or
-homogeneous leftmonogenic
function, for
or
, respectively, and h is a function defined in [0,∞) satisfying a certain integrability condition in relation to k, the spaces
are invariant under Fourier transformation.
This extends the classical result for
. We also deduce explicit Fourier transform
formulas for functions of the form
refining Bochner’s formula for spherical k-harmonics. 相似文献
10.
We continue the investigation of some problems in learning theory in the setting formulated by F. Cucker and S. Smale. The
goal is to find an estimator
on the base of given data
that approximates well the regression function
of an unknown Borel probability measure
defined on
We assume that
belongs to a function class
It is known from previous works that the behavior of the entropy numbers
of
in the uniform norm
plays an important role in the above problem. The standard way of measuring the error between a target function
and an estimator
is to use the
norm (
is the marginal probability measure on X generated by
). This method has been used in previous papers. We continue to use this method in this paper. The use of the
norm in measuring the error has motivated us to study the case when we make an assumption on the entropy numbers
of
in the
norm. This is the main new ingredient of thispaper. We construct good estimators in different settings: (1) we know both
and
; (2) we know
but we do not know
and (3) we only know that
is from a known collection of classes but we do not know
An estimator from the third setting is called a universal estimator. 相似文献
11.
Nonlinear Approximation by Trigonometric Sums 总被引:7,自引:0,他引:7
We investigate the
-error of approximation to a function
by a linear combination
of
exponentials
on
where the frequencies
are allowed to depend on
We bound this error in terms of the smoothness and other properties of
and show that our bounds are best possible in the sense of approximation of certain classes of functions. 相似文献
12.
In this article we show that the distributional point values of a tempered distribution are characterized by their Fourier
transforms in the following way: If
and
, and
is locally integrable, then
distributionally if and only if there exists k such that
, for each a > 0, and similarly in the case when
is a general distribution. Here
means in the Cesaro sense. This result generalizes the characterization of Fourier series of distributions with a distributional
point value given in [5] by
. We also show that under some extra conditions, as if the sequence
belongs to the space
for some
and the tails satisfy the estimate
,\ as
, the asymmetric partial sums\ converge to
. We give convergence results in other cases and we also consider the convergence of the asymmetric partial integrals. We
apply these results to lacunary Fourier series of distributions. 相似文献
13.
We show that every function in the Hardy space can be approximated by linear combinations of translates and dilates of a synthesizer
, provided only that
and
satisfies a mild regularity condition. Explicitly, we prove scale averaged approximation for each
,
where
is an arbitrary lacunary sequence (such as
) and the coefficients
are local averages of f. This formula holds in particular if the synthesizer
is in the Schwartz class, or if it has compact support and belongs to
for some
in terms of differences of
. 相似文献
14.
C. Carton-Lebrun 《Journal of Fourier Analysis and Applications》1995,2(1):49-64
For
define
where
Pointwise estimates and weighted inequalities describing the local Lipschitz continuity
of
are established. Sufficient conditions are found
for the boundedness of
from
into
and a spherical restriction property is proved. A study of the moment subspaces of
is next developed in the one-variable case, for
locally integrable,
a.e. It includes a decomposition theorem and a complete classification of all possible sequences of moment subspaces in
Characterizations are also given for each class. Applications related to the approximation and decomposition of
are discussed. 相似文献
15.
A.J.E.M. Janssen 《Journal of Fourier Analysis and Applications》1994,1(4):403-436
Let
and let
In this paper we investigate the relation between the frame operator
and the matrix
whose entries
are given by
for
Here
, for any
We show that
is bounded as a mapping of
into
if and only if
is bounded as a mapping of
into
Also we show that
if and
only if
where
denotes the identity operator of
and
respectively, and
Next, when
generates a frame, we have that
has an upper frame bound, and the minimal dual function
can be computed as
The results of this paper extend, generalize, and rigourize results of Wexler and Raz and of Qian, D. Chen, K. Chen, and
Li on the computation of dual functions for finite, discrete-time Gabor expansions to the infinite, continuous-time case.
Furthermore, we present a framework in which one can show that certain smoothness and decay properties of a
generating a frame are inherited by
In particular, we show that
when
generates a frame
Schwartz space). The proofs of the main results of this paper rely heavily on a technique introduced by Tolimieri and Orr
for relating frame bound questions on complementary lattices by means of the Poisson summation formula. 相似文献
16.
For each integer n 2, let
be the index of composition of n, where
. For convenience, we write (1)=(1)=1. We obtain sharp estimates for
and
, as well as for
and
. Finally we study the sum of running over shifted primes.Research supported in part by a grant from NSERC.Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA. 相似文献
17.
David Walnut 《Journal of Fourier Analysis and Applications》1995,2(5):435-452
It is shown that a function
is completely determined by the samples of
on sets
where
and
is irrational if
and of
If
then the samples of
on
and only the first k derivatives of
at 0 are required to determine f completely. Higher dimensional analogues of these results, which apply to functions
and
are proven. The sampling results are sharp in the sense that if any condition is omitted, there exist nonzero
and
satisfying the rest. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials
that are not Riesz bases for
A signal processing application in which such sampling sets arise naturally is described in detail. 相似文献
18.
Sadahiro Saeki 《Journal of Fourier Analysis and Applications》1995,2(1):15-28
Let
and
Under certain conditions on
we shall prove that
converges nontangentially to
at
for
相似文献
19.
David Hernandez 《Transformation Groups》2005,10(2):163-200
In this paper we
study general quantum affinizations
of symmetrizable quantum Kac-Moody algebras and we
develop their representation theory. We prove a
triangular decomposition and we give a classication
of (type 1) highest weight simple integrable
representations analog to Drinfel'd-Chari-Presley
one. A generalization of the q-characters
morphism, introduced by Frenkel-Reshetikhin for
quantum affine algebras, appears to be a powerful
tool for this investigation. For a large class of
quantum affinizations (including quantum affine
algebras and quantum toroidal algebras), the
combinatorics of q-characters give a ring
structure * on the Grothendieck group
of the integrable representations that we
classified. We propose a new construction of tensor
products in a larger category by using the
Drinfel'd new coproduct (it cannot directly be
used for
because it involves infinite sums). In particular,
we prove that * is a fusion product (a product of
representations is a representation). 相似文献
20.
Ka-Sing Lau 《Journal of Fourier Analysis and Applications》1995,2(4):397-406
We prove a Tauberian theorem of the form
as
where p(x) is a bounded periodic function and w(x) is a weighted function of power growth. It can be used to study the weighted
average of the form
相似文献