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1.
Huoxiong Wu 《Integral Equations and Operator Theory》2005,52(2):285-298
This paper is devoted to the study on the Lp-mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on
The
boundedness of the Marcinkiewicz integrals for some fixed 1 < p < ∞ are obtained under some size conditions, which essentially improve or extend some well-known results. 相似文献
2.
The fiberization of affine systems via dual Gramian techniques, which was developed in previous papers of the authors, is
applied here for the study of affine frames that have an affine dual system. Gramian techniques are also used to verify whether
a dual pair of affine frames is also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a
dual pair of affine frames from an arbitrary MRA is obtained via the mixed extension principle.
This work was partially sponsored by the National Science Foundation under Grants DMS-9102857, DMS-9224748, and DMS-9626319,
by the United States Army Research Office under Contracts DAAL03-G-90-0090, DAAH04-95-1-0089, and by the Strategic Wavelet
Program Grant from the National University of Singapore. 相似文献
3.
L
p
mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translated of a real-analytic submanifold in R
n
.Work in this paper was done during the second author's visit at the Department of Mathematics, University of Pittsburgh.Supported in part by NSF Grant DMS-9622979. 相似文献
4.
It is proved that a lacunary sequence of the Ciesielski-Fourier series of
converges almost everywhere to f.
Received: 8 September 2003 相似文献
5.
Ezio Araujo de Costa 《Archiv der Mathematik》2008,90(1):82-86
In this paper we obtain a classification of compact n-submanifolds of the Euclidean space with 2-nonnegative curvature operator.
Received: 4 April 2007 相似文献
6.
Jürgen J. Voss 《Journal of Fourier Analysis and Applications》1999,5(2-3):193-201
It is well known that for certain sequences {tn}n the usual Lp norm ·p in the Paley-Wiener space PW
p
is equivalent to the discrete norm fp,{tn}:=(
n=–
|f(tn)|p)1/p for 1 p = < and f,{tn}:=sup
n|f(tn| for p=). We estimate fp from above by Cfp,
n
and give an explicit value for C depending only on p, , and characteristic parameters of the sequence {tn}n. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer. 相似文献
7.
Stability theorems for Fourier frames and wavelet Riesz bases 总被引:4,自引:0,他引:4
Radu Balan 《Journal of Fourier Analysis and Applications》1997,3(5):499-504
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet
Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and
Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis, our estimate reduces
to Kadec’ optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian [4]
for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter)
actually holds for a large class of wavelet Riesz bases. 相似文献
8.
9.
Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Köthe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider the Y-bidual space XYY of X (i.e. the Y-dual of XY). As in the classical case, the containment X ⊂ XYY always holds. We give conditions guaranteeing that X coincides with XYY, in which case X is said to be Y-perfect. We also study when X is isometrically embedded in XYY. Properties involving p-convexity, p-concavity and the order of X and Y, will have a special relevance. 相似文献
10.
Tuomas P. Hytönen 《Journal of Evolution Equations》2005,5(2):205-225
We extend the recently developed Lp-theory for the maximal regularity of the abstract Cauchy problem
and the related Fourier multiplier techniques to the real-variable Hardy space H1. Some results for Hp, 0 < p < 1, are also proved. 相似文献
11.
Richard Vale 《Linear algebra and its applications》2010,433(1):248-94
We define the symmetry group of a finite frame as a group of permutations on its index set. This group is closely related to the symmetry group of Vale and Waldron (2005) [12] for tight frames: they are isomorphic when the frame is tight and has distinct vectors. The symmetry group is the same for all similar frames, in particular for a frame, its dual and canonical tight frames. It can easily be calculated from the Gramian matrix of the canonical tight frame. Further, a frame and its complementary frame have the same symmetry group. We exploit this last property to construct and classify some classes of highly symmetric tight frames. 相似文献
12.
W.S. Cheung 《Linear algebra and its applications》2010,432(1):107-115
In this paper, we shall follow a companion matrix approach to study the relationship between zeros of a wide range of pairs of complex polynomials, for example, a polynomial and its polar derivative or Sz.-Nagy’s generalized derivative. We shall introduce some new companion matrices and obtain a generalization of the Weinstein-Aronszajn Formula which will then be used to prove some inequalities similar to Sendov conjecture and Schoenberg conjecture and to study the distribution of equilibrium points of logarithmic potentials for finitely many discrete charges. Our method can also be used to produce, in an easy and systematic way, a lot of identities relating the sums of powers of zeros of a polynomial to that of the other polynomial. 相似文献
13.
J. William Helton Orlando Merino Trent E. Walker 《Integral Equations and Operator Theory》1995,22(4):420-439
This article gives necessary and sufficient conditions for local solutions to several very general constrained optimization problems over spaces of analytic functions.The results presented here have many applications, a particular instance of which is the sup-norm approximation of functions continuous on the unit circle in the complex plane by functions continuous on the circle and analytic on the open disk and whose Fourier coefficients satisfy prescribed linear relations.Also, the results in this article generalize Nevanlinna-Pick and Caratheodory-Fejer Interpolation results to allow values of arbitrary derivatives of functions to be assigned or merely bounded. Classically, NP and CF solve only problems with consecutive derivatives specified.In engineering, constraints on the Fourier coefficients of a frequency response function correspond to constraints on its time domain behavior. Indeed the central problems of control theory involve both time and frequency domain constraints. That is precisely what the results in this paper handle.Supported in part by the AFOSR and the NSF 相似文献
14.
15.
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
16.
An algorithmic solution to Teichmüller's extremal ring problem is given. 相似文献
17.
E. Preissmann 《Aequationes Mathematicae》1987,32(1):195-212
We solve independently the equations 1/θ(x)θ(y)=ψ(x)−ψ(y)+φ(x−y)/θ(x−y) and 1/θ(x)θ(y)=σ(x)−σ(y)/θ(x−y)+τ(x)τ(y), τ(0)=0. In both cases we find θ2=aθ4+bθ2+c. We deduce estimates for the spectral radius of a matrix of type(1/θ(x
r
−x
s
)) (the accent meaning that the coefficients of the main diagonal are zero) and we study the case where thex
r
are equidistant.
Dédié to à Monsieur le Professeur Otto Haupt à l'occasion de son cententiare avec les meilleurs voeux 相似文献
18.
Tord Sjödin 《Mathematische Annalen》2007,337(2):317-333
We prove weighted L
p
-inequalities for multi-parameter Riesz type potentials, strong fractional maximal operators and their dyadic counterparts. Our proofs avoid the Good-λ inequalities used earlier in the R
m
-case and are based on our integrated multi-parameter summation by parts lemma, that might be of independent interest. 相似文献
19.
In this paper we prove that a compact oriented hypersurface of a Euclidean
sphere with nonnegative Ricci curvature and infinite fundamental group is isometric
to an H(r)-torus
with constant mean curvature. Furthermore, we generalize, whithout any
hypothesis about the mean curvature, a characterization of Clifford torus due to
Hasanis and Vlachos.
Received: 19 March 2002 相似文献
20.
The paper deals with sampling of σ-bandlimited functions in Rm with Clifford-valued, where bandlimitedness means that the spectrum is contained in the ball B(0, σ) that is centered at the origin and has radius σ. By comparing with the general setting, what is new in the sampling is using the explicit Bochner-type relations involving
spherical harmonics and monogenics in the Clifford algebra setting. Convergence of the sampling formulas in the L2 sense and in the uniform and absolute pointwise sense are studied.
The study was supported by Research Grant of the University of Macau No. RG059/05- 06S/QT/FST. 相似文献