共查询到20条相似文献,搜索用时 31 毫秒
1.
Óscar Ciaurri Juan L. Varona 《Journal of Computational and Applied Mathematics》2010,233(6):1499-1504
An uncertainty inequality for the Fourier-Dunkl series, introduced by the authors in [Ó. Ciaurri, J.L. Varona, A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Dunkl transform, Proc. Amer. Math. Soc. 135 (2007) 2939-2947], is proved. This result is an extension of the classical uncertainty inequality for the Fourier series. 相似文献
2.
Elena A. Lebedeva 《Applied and Computational Harmonic Analysis》2017,42(3):536-549
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A particular minimization problem for a non-periodic (Heisenberg) uncertainty constant is studied. 相似文献
3.
Jizheng Huang 《Bulletin des Sciences Mathématiques》2009,133(6):588-596
In this paper, we will consider the boundedness of Weyl multiplier on Hardy spaces associated with twisted convolution. In order to get our result, we need to give some characterizations of the Hardy space associated with twisted convolution. Including Lusin area integral, Littlewood-Paley g-function. 相似文献
4.
We prove a Calderón reproducing formula for a continuous wavelet transform associated with a class of singular differential
operators on the half line. We apply this result to derive a new inversion formula for the generalized Abel transform. 相似文献
5.
PONStm is a basis which satisfies all of the fundamental properties of the Walsh functions (each element is piecewise constant,
takes on only the values ±1, and can be efficiently computed via a fast transform) plus three additional properties that are
false for the Walsh functions: PONS is optimal with respect to a global uncertainty principle; all PONS elements have uniformly
bounded crest factors; and all PONS elements are QMF’s. In 1991, Ingrid Daubechies asked whether there exists a smooth basis
satisfying the global uncertainty principle property. In this article we show how to transform any basis into another basis
by applying the PONS construction, thereby providing an affirmative answer to this question. 相似文献
6.
Richard J. Duffin Hans F. Weinberger 《Journal of Fourier Analysis and Applications》1997,3(5):487-497
It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ø of one variable into a function and its cosine transform in a generalized sense. The present work presents conditions on ø for which the transform relation holds in the classical sense, and extends this result to a class of generalizations of the Poisson formula in any number of dimensions. 相似文献
7.
Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces 总被引:1,自引:0,他引:1
Under the appropriate definition of sampling density Dϕ, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only
if Dϕ≥1. This result is similar to Landau's result for the Paley-Wiener space B
1/2
. If the shift invariant space consists of polynomial splines, then we show that Dϕ<1 is sufficient for the stable reconstruction of a function f from its samples, a result similar to Beurling's special case
B
1/2
. 相似文献
8.
The uncertainty principle: A mathematical survey 总被引:1,自引:0,他引:1
We survey various mathematical aspects of the uncertainty principle, including Heisenberg’s inequality and its variants, local
uncertainty inequalities, logarithmic uncertainty inequalities, results relating to Wigner distributions, qualitative uncertainty
principles, theorems on approximate concentration, and decompositions of phase space. 相似文献
9.
By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of k
–1 cosk. 相似文献
10.
Periodization and sampling operators are defined, and the Fourier transform of periodization is uniform sampling in a well-defined
sense. Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions
of bounded variation (where the result is known) and elements of mixed norm spaces. These Poisson Summation Formulas can be
used to prove corresponding sampling theorems.
The sampling operators used to understand and prove the aforementioned Poisson Summation Formulas lead to the introduction
of spaces of continuous linear operators which commute with integer translations. Operators L of this type are appropriately
called sampling multipliers. For a given function f, they give rise to new sampling formulas, whose sampling coefficients
are of the form Lf. In practice, Lf can be used to model noisy data or data where point values are not available. By representation
theorems of the second named author, some of these operator spaces are proved to be mixed norm spaces.
The approach and results of this paper were developed in the context of Duffin and Schaeffer’s theory of frames. In particular,
sampling multipliers L are related to the Bessel map used by Duffin and Schaeffer in their definition of the frame operator.
The first named author was supported in part by AFOSR contract F49620-96-1-0193.
The second named author was supported by the Cusanuswerk. 相似文献
11.
Hông Vân Lê 《Journal of Geometry》2006,84(1-2):83-93
In this note we prove that any smooth (C1 resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get positive
answers to Lauritzen’s question and Amari’s question on a realization of smooth (C1 resp.) statistical manifolds as finite dimensional statistical models. 相似文献
12.
We generalize the Ap extrapolation theorem of Rubio de Francia to A∞ weights in the context of Muckenhoupt bases. Our result has several important features. First, it can be used to prove weak endpoint inequalities starting from strong-type inequalities, something which is impossible using the classical result. Second, it provides an alternative to the technique of good-λ inequalities for proving Lp norm inequalities relating operators. Third, it yields vector-valued inequalities without having to use the theory of Banach space valued operators. We give a number of applications to maximal functions, singular integrals, potential operators, commutators, multilinear Calderón-Zygmund operators, and multiparameter fractional integrals. In particular, we give new proofs, which completely avoid the good-λ inequalities, of Coifman's inequality relating singular integrals and the maximal operator, of the Fefferman-Stein inequality relating the maximal operator and the sharp maximal operator, and the Muckenhoupt-Wheeden inequality relating the fractional integral operator and the fractional maximal operator. 相似文献
13.
This paper is on the angle–frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty
products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from
above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration,
scaling functions and wavelets associated with a family of generalized periodic splines are studied. This family is generated
by periodic weighted convolutions, and it includes the well‐known periodic B‐splines and trigonometric B‐splines.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
Albert Borbély 《Differential Geometry and its Applications》2008,26(6):667-675
A recent result of Tobias Ekholm [T. Ekholm, Regular homotopy and total curvature II: Sphere immersions into 3-space, Alg. Geom. Topol. 6 (2006) 493-513] shows that for every ?>0 it is possible to construct a sphere eversion such that the total absolute curvature of the immersed spheres are always less than 8π+?. It is an open question whether this is the best possible. The paper contains results relating to this conjecture. As an interesting consequence of these methods it is shown that if during an eversion the total absolute curvature does not exceed 12π then a certain topological event must take place, namely the immersion must become non-simple at some point. An immersion f in general position is simple if for any irreducible self-intersection curve of f in 3-space, its two pre-image curves in the sphere are disjoint. 相似文献
15.
In this article we give some new necessary conditions for subsets of the unit circle to give collections of rectangles (by
means of orientations) which differentiate Lp-functions or give Hardy-Littlewood type maximal functions which are bounded on Lp, p>1. This is done by proving that a well-known method, the construction of a Perron Tree, can be applied to a larger collection
of subsets of the unit circle than was earlier known. As applications, we prove a partial converse of a well-known result
of Nagel et al. [6] regarding boundedness of maximal functions with respect to rectangles of lacunary directions, and prove
a result regarding the cardinality of subsets of arithmetic progressions in sets of the type described above.
Acknowledgements and Notes. This research was partially supported by NSERC. 相似文献
16.
James E. Daly 《Journal of Fourier Analysis and Applications》1999,5(4):303-308
Calderón-Zygmund singular integral operators have been extensively studied for almost half a century. This paper provides a context for and proof of the following result: If a Calderón-Zygmund convolution singular integral operator is bounded on the Hardy space H1 (Rn), then the homogeneous of degree zero kernel is in the Hardy space H1(Sn–1) on the sphere. 相似文献
17.
An open problem in the theory of Fourier series is whether there are functions f L
1 such that the partial sums S
n(f, x) diverge faster than log log n, almost everywhere in x. For a class of particularly bad functions Kahane proved that the rate of divergence is faster than o(log log n). We give here a probabilistic interpretation of the Kahane result, which shows that the record values of the sums S
n(f, x) should behave essentially as the record values of a sequence of independent identically distributed random variables, for which we deduce the divergence rate log log n. Numerical computation is in good agreement with the prediction. One can argue that the Kahane examples are in some sense optimal, and conclude that, under this assumption, ...(log log n) is the highest possible rate for divergence almost everywhere of the Fourier partial sums for L
1 functions. 相似文献
18.
This article proves the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem
establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly
at its vertex. It thus unifies earlier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert
transform of Lacey-Thiele, where the multiplier is not smooth. Using a Whitney decomposition in the Fourier plane, a general
bilinear operator is represented as infinite discrete sums of time-frequency paraproducts obtained by associating wave-packets
with tiles in phase-plane. Boundedness for the general bilinear operator then follows once the corresponding Lp-boundedness of time-frequency paraproducts has been established. The latter result is the main theorem proved in Part in
Part II, our subsequent article [11], using phase-plane analysis.
In memory of A.P. Calderón 相似文献
19.
T. Tevzadze 《Georgian Mathematical Journal》1996,3(4):379-400
The estimate of the modulus of smoothness of an even function of several variables with quasiconvex fourier coefficients obtained in this paper extends one result of S. A. Telyakovski. 相似文献
20.
Steven Delvaux 《Linear algebra and its applications》2008,429(7):1587-1605
We consider the maximal rank-deficient submatrices of Fourier matrices with order a power of a prime number. We do this by considering a hierarchical subdivision of these matrices into low rank blocks. We also explore some connections with the fast Fourier transform (FFT), and with an uncertainty principle for Fourier transforms over finite Abelian groups. 相似文献