共查询到20条相似文献,搜索用时 0 毫秒
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Steffen Fröhlich 《Differential Geometry and its Applications》2005,23(3):235-256
We consider two-dimensional immersions in Euclidean 3-space that are stable for parametric functionals of constant mean curvature type. We develop analytical and geometric concepts to give a perturbation result to estimate the principle curvatures of such mappings via uniformization. 相似文献
3.
We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy
superior resolution provided the data is globally smooth, while the presence of jump discontinuities is responsible for spurious
O (1) Gibbs oscillations in the neighborhood of edges and an overall deterioration of the unacceptable first-order convergence
in rate. The purpose is to regain the superior accuracy in the piecewise smooth case, and this is achieved by mollification.
Here we utilize a modified version of the two-parameter family of spectral mollifiers introduced by Gottlieb and Tadmor [GoTa85].
The ubiquitous one-parameter, finite-order mollifiers are based on dilation . In contrast, our mollifiers achieve their high resolution by an intricate process of high-order cancellation . To this end, we first implement a localization step using an edge detection procedure [GeTa00a, b]. The accurate recovery
of piecewise smooth data is then carried out in the direction of smoothness away from the edges, and adaptivity is responsible for the high resolution. The resulting adaptive mollifier greatly accelerates the convergence rate, recovering
piecewise analytic data within exponential accuracy while removing the spurious oscillations that remained in [GoTa85]. Thus,
these adaptive mollifiers offer a robust, general-purpose ``black box' procedure for accurate post-processing of piecewise
smooth data.
March 29, 2001. Final version received: August 31, 2001. 相似文献
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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.
In this paper, we are concerned with biorthogonal Wilson bases having B-splines as well as powers of sinc functions as window functions. We prove properties of B-splines and exponential Euler splines and use these properties to estimate the Riesz bounds of the Wilson bases. 相似文献
7.
M. Khazaradze 《Georgian Mathematical Journal》1996,3(2):121-132
The theorem on the tending to zero of coefficients of a trigonometric series is proved when theL
1-norms of partial sums of this series are bounded. It is shown that the analog of Helson's theorem does not hold for orthogonal series with respect to the bounded orthonormal system. Two facts are given that are similar to Weis' theorem on the existence of a trigonometric series which is not a Fourier series and whoseL
1-norms of partial sums are bounded. 相似文献
8.
《Quaestiones Mathematicae》2013,36(1):77-81
The concept of a structural matrix ring was introduced by van Wyk [8]. In [9] certain radicals of these matrix rings are studied. The purpose of this paper is to obtain similar results for a wider class of radicals. 相似文献
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We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz-Toeplitz isometries as a special case. 相似文献
10.
This article concerns the stability of orthogonal bases of solutions of Sturm-Liouville equations with different types of initial conditions. The investigation is based on the stability of Riesz bases of cosines and sines in the Hibert space L2[0,π]. 相似文献
11.
E. S. Belinskii E. R. Liflyand R. M. Trigub 《Journal of Fourier Analysis and Applications》1997,3(2):103-129
Beurling’s algebra
is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener’s
algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means.
Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain
essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with[−π, π], and its dual space is indicated. Analogs of Herz’s and Wiener-Ditkin’s theorems hold. Quantitative parameters in an analog
of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach
spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis
are presented. The paper ends with a summary of some open problems. 相似文献
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In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Gröbner-Shirshov bases of free Rota-Baxter algebra, free λ-differential algebra and free λ-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar to the recent results obtained by K. Ebrahimi-Fard-L. Guo, and L. Guo-W. Keigher by using other methods. 相似文献
14.
On the stability of wavelet and Gabor frames (Riesz bases) 总被引:6,自引:0,他引:6
Zhang Jing 《Journal of Fourier Analysis and Applications》1999,5(1):105-125
If the sequence of functions j, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system j,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of or
is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16]. 相似文献
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A necessary and sufficient condition is given for approximation with weighted expressions of the form wnPn, where w is a given continuous weight function and Pn are polynomials of degree . The condition is that the extremal measure that solves an associated equilibrium problem is smooth (asymptotically optimal doubling). As corollaries we get all previous (positive and negative) results for approximation, as well as the solution of a problem of T. Bloom and M. Branker. A connection to level curves of homogeneous polynomials of two variables is also explored. 相似文献
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《Quaestiones Mathematicae》2013,36(1):7-15
ABSTRACT In this note, we define the antisimple radical, A(M), of a Γ-ring M. A(M) is shown to be a special radical, and two characterizations of antisimple rings due to Szész are extended to Γ-rings. If R is the right operator ring of M, then A(R)* = A(M), where A(R) is the antisimple radical of R. If m,n are positive integers, then A(Mmn) = (A(M))mn, where Mmn denotes the group m x n matrices over M, considered as a Γnm -ring with the operations of matrix addition and multiplication. 相似文献
18.
We characterize, for finite measure spaces, those orthonormal bases with the following positivity property: if f is a non-negative
function, then the partial sums in the expansion of f are non-negative. The bases are necessarily generalized Haar functions
and the partial sums are a martingale closed on the right by f. 相似文献
19.
Vladimír Müller 《Integral Equations and Operator Theory》2007,57(2):229-234
We exhibit an example of a bounded linear operator on a Banach space which admits an everywhere defined local resolvent with
continuous derivatives of all orders. 相似文献
20.
In this paper we show that the number of pairwise nonisomorphic two-dimensional posets with n elements is asymptotically equivalent to 1/2n!. This estimate is based on a characterization, in terms of structural decomposition, of two-dimensional posets having a unique representation as the intersection of two linear extensions. 相似文献