共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions.
We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions. 相似文献
2.
We state a localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator and we prove an equiconvergence result between eigenfunction expansions and trigonometric expansions. We then study the Gibbs phenomenon for eigenfunction expansions of piecewise smooth functions on two-dimensional manifolds. 相似文献
3.
We introduce a class of continued fraction expansions called Oppenheim continued fraction (OCF) expansions. Basic properties of these expansions are discussed and metric properties of the digits occurring in the OCF expansions are studied. 相似文献
4.
Amanda Folsom 《Journal of Number Theory》2006,117(2):279-291
Found in the collected works of Eisenstein are twenty continued fraction expansions. The expansions have since emerged in the literature in various forms, although a complete historical account and self-contained treatment has not been given. We provide one here, motivated by the fact that these expansions give continued fraction expansions for modular forms. Eisenstein himself did not record proofs for his expansions, and we employ only standard methods in the proofs provided here. Our methods illustrate the exact recurrence relations from which the expansions arise, and also methods likely similar to those originally used by Eisenstein to derive them. 相似文献
5.
Kun Chuan Wang 《数学学报(英文版)》2008,24(7):1107-1116
We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2(R). As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expansions generated by translations and dilation. 相似文献
6.
Vladimir Temlyakov 《Journal of Fourier Analysis and Applications》2007,13(1):71-86
We study greedy algorithms in a Banach space from the point of view of convergence and rate of convergence. We concentrate
on studying algorithms that provide expansions into a series. We call such expansions greedy expansions. It was pointed out
in our previous article that there is a great flexibility in choosing coefficients of greedy expansions. In that article this
flexibility was used for constructing a greedy expansion that converges in any uniformly smooth Banach space. In this article
we push the flexibility in choosing the coefficients of greedy expansions to the extreme. We make these coefficients independent
of an element f ∈ X. Surprisingly, for a properly chosen sequence of coefficients we obtain results similar to the previous
results on greedy expansions when the coefficients were determined by an element f. 相似文献
7.
We investigate metric properties of the polynomial digits occurring in a large class of Oppenheim expansions of Laurent series, including Lüroth, Engel, and Sylvester expansions of Laurent series and Cantor infinite products of Laurent series. The obtained results cover those for special cases of Lüroth and Engel expansions obtained by Grabner, A. Knopfmacher, and J. Knopfmacher. Our results applied in the cases of Sylvester expansions and Cantor infinite products are original. We also calculate the Hausdorff dimensions of different exceptional sets on which the above-mentioned metric properties fail to hold. 相似文献
8.
N. Yu. Kapustin 《Differential Equations》2012,48(5):701-706
We study issues related to the uniform convergence of the Fourier series expansions of Hölder class functions in the system of eigenfunctions corresponding to a spectral problem obtained from a mixed problem for the heat equation. We prove a theorem on the equiconvergence of these expansions with expansions in a well-known orthonormal basis. 相似文献
9.
Christopher S. Withers Saralees Nadarajah 《Methodology and Computing in Applied Probability》2014,16(3):693-713
We give expansions for the distribution, density, and quantiles of an estimate, building on results of Cornish, Fisher, Hill, Davis and the authors. The estimate is assumed to be non-lattice with the standard expansions for its cumulants. By expanding about a skew variable with matched skewness, one can drastically reduce the number of terms needed for a given level of accuracy. The building blocks generalize the Hermite polynomials. We demonstrate with expansions about the gamma. 相似文献
10.
Yuichi Kanjin 《Journal of Fourier Analysis and Applications》2013,19(3):495-513
We establish Wiener type theorems and Paley type theorems for Laguerre polynomial expansions and disk polynomial expansions with nonnegative coefficients. 相似文献
11.
I. S. Lomov 《Differential Equations》2014,50(8):1070-1079
We study the convergence rate of biorthogonal series expansions of functions in systems of root functions of a broad class of loaded even-order differential operators defined on a finite interval. These expansions are compared with the Fourier trigonometric series expansions of the same functions in an integral metric on any interior compact set of the main interval or on the entire interval. We obtain estimates for the equiconvergence rate of these expansions. 相似文献
12.
We find sharp conditions for the pointwise convergence ofeigenfunction expansions associated with the Laplace operator and otherrotationally invariant differential operators. Specifically, we considerthis problem for expansions associated with certain radially symmetricoperators and general boundary conditions and the problem in the contextof Jacobi polynomial expansions. The latter has immediate application toFourier series on rank one symmetric spaces of compact type. 相似文献
13.
We study an extension of the classical Paley–Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier–Neumann type series as special cases, and it also provides a bilinear expansion for the Dunkl kernel (in the rank 1 case) which is a Dunkl analogue of Gegenbauer’s expansion of the plane wave and the corresponding sampling expansions. In fact, we show how to derive sampling and Fourier–Neumann type expansions from the results related to the bilinear expansion for the Dunkl kernel. 相似文献
14.
Stochastic expansions of likelihood quantities are usually derived through oridinary Taylor expansions, rearranging terms
according to their asymptotic order. The most convenient form for such expansions involves the score function, the expected
information, higher order log-likelihood derivatives and their expectations. Expansions of this form are called expected/observed.
If the quantity expanded is invariant or, more generally, a tensor under reparameterisations, the entire contribution of a
given asymptotic order to the expected/observed expansion will follow the same transformation law. When there are no nuisance
parameters, explicit representations through appropriate tensors are available. In this paper, we analyse the geometric structure
of expected/observed likelihood expansions when nuisance parameters are present. We outline the derivation of likelihood quantities
which behave as tensors under interest-respectign reparameterisations. This allows us to write the usual stochastic expansions
of profile likelihood quantities in an explicitly tensorial form. 相似文献
15.
Roberto Avanzi Waldyr Dias BenitsJr Steven D. Galbraith James McKee 《Designs, Codes and Cryptography》2011,61(1):71-89
Frobenius expansions are representations of integers to an algebraic base which are sometimes useful for efficient (hyper)elliptic
curve cryptography. The normal form of a Frobenius expansion is the polynomial with integer coefficients obtained by reducing
a Frobenius expansion modulo the characteristic polynomial of Frobenius. We consider the distribution of the coefficients
of reductions of Frobenius expansions and non-adjacent forms of Frobenius expansions (NAFs) to normal form. We give asymptotic
bounds on the coefficients which improve on naive bounds, for both genus one and genus two. We also discuss the non-uniformity
of the distribution of the coefficients (assuming a uniform distribution for Frobenius expansions). 相似文献
16.
I. S. Lomov 《Differential Equations》2010,46(10):1415-1426
We consider the problem on the convergence rate of biorthogonal expansions of functions in systems of root functions of a
wide class of ordinary second-order differential operators defined on a finite interval. These expansions are compared with
expansions of the same functions in Fourier trigonometric series in an integral or uniform metric on any interior compact
subset of the main interval. We find the dependence of the equiconvergence rate of resulting expansions on the distance from
the compact set to the boundary of the interval, on the coefficients of the differential operation, and on the presence of
infinitely many associated functions in the system of root functions. 相似文献
17.
Estimates of the local convergence rate of spectral expansions for even-order differential operators
We study the convergence rate of biorthogonal series expansions of functions in systems of root functions of a wide class of even-order ordinary differential operators defined on a finite interval. These expansions are compared with the trigonometric Fourier series expansions of the same functions in the integral or uniform metric on an arbitrary interior compact set of the main interval as well as on the entire interval. We show the dependence of the equiconvergence rate of these expansions on the distance from the compact set to the boundary of the interval, on the coefficients of the differential operation, and on the existence of infinitely many associated functions in the system of root functions. 相似文献
18.
J. G. Byatt-Smith 《Studies in Applied Mathematics》1999,103(4):339-369
The solution of connection problems on the real line (the x axis) often give asymptotic expansions which are either even or odd. This gives rise to 'identically zero' expansions, that is, an asymptotic expansion in which all terms are identically zero at the origin. We show that the Borel transform of these problems have solutions that provide integral representations of the solution. The evaluation of these integrals, as x →0, allows us to compute the exponentially small term that these 'identically zero' expansions represent. 相似文献
19.
We consider asymptotic expansions for defective and excessive renewal equations that are close to being proper. These expansions are applied to the analysis of processor sharing queues and perturbed risk models, and yield approximations that can be useful in applications where moments are computable, but the distribution is not. 相似文献
20.
J. G. Byatt-Smith 《Studies in Applied Mathematics》2000,105(2):83-113
The solution of connection problems on the real line (the x axis) often give asymptotic expansions which are either even or odd. This gives rise to "identically zero" expansions, that is, an asymptotic expansion in which all terms are identically zero at the origin. We show that the Borel transform of these problems have solutions that provide integral representations of the solution. The evaluation of these integrals, as x →0, allows us to compute the exponentially small term that these "identically zero" expansions represent. 相似文献