共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper is devoted to investigating the solutions of refinement equations of the form Ф(x)=∑α∈Z^s α(α)Ф(Mx-α),x∈R^s,where the vector of functions Ф = (Ф1,… ,Фr)^T is in (L1(R^s))^r, α =(α(α))α∈Z^s is an infinitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M^-n =0, with m = detM. Some properties about the solutions of refinement equations axe obtained. 相似文献
2.
Song LI~ 《中国科学A辑(英文版)》2007,50(7):1015-1025
Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form (?)(x)=(?)a(α)(?)(Mx-α),x∈R~s, where the vector of functions(?)=((?)_1,...,(?)_r)~T is in(L_2(R~s))~r,a=:(a(α))_(α∈Z~s)is a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim_(n→∞)M~(-n)=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results. 相似文献
3.
Liu Zhisong 《高校应用数学学报(英文版)》2007,22(3):299-310
In this paper,some characterizations on the convergence rate of both the homoge- neous and nonhomogeneous subdivision schemes in Sobolev space are studied and given. 相似文献
4.
Song Li 《Advances in Computational Mathematics》2004,20(4):311-331
This paper concerns multivariate homogeneous refinement equations of the form
and multivariate nonhomogeneous refinement equations of the form
where =(1,...,
r
)T is the unknown, M is an s×s dilation matrix with m=|detM|, g=(g
1,...,g
r
)T is a given compactly supported vector-valued function on R
s
, and a is a finitely supported refinement mask such that each a() is an r×r (complex) matrix. In this paper, we characterize the optimal smoothness of a multiple refinable function associated with homogeneous refinement equations in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite-dimensional invariant subspace when M is an isotropic dilation matrix. Nonhomogeneous refinement equations naturally occur in multi-wavelets constructions. Let 0 be an initial vector of functions in the Sobolev space (W
2
k
(R
s
))
r
(kN). The corresponding cascade algorithm is given by
相似文献
5.
In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks. 相似文献
6.
In this paper, we investigate the support of a refinable vector satisfying an inhomoge- neous refinement equation. By using some methods introduced by So and Wang, an estimate is given for the support of each component function of a compactly supported refinable vector satisfying an inhomogeneous matrix refinement equation with finitely supported masks. 相似文献
7.
Yang Wang 《Journal of Approximation Theory》2001,113(2):207
We consider the two-scale refinement equation f(x)=∑Nn=0 cnf(2x−n) with ∑n c2n=∑n c2n+1=1 where c0, cN≠0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn0. It has long been conjectured that under such an assumption the subdivision algorithm converge, and the cascade algorithm converge uniformly to a continuous function, if and only if only if 0<c0, cN<1 and the greatest common divisor of S={n: cn>0} is 1. We prove the conjecture for a large class of refinement equations. 相似文献
8.
We consider the Itô stochastic differential equation on Rd. The diffusion coefficients A1,…,Am are supposed to be in the Sobolev space with p>d, and to have linear growth. For the drift coefficient A0, we distinguish two cases: (i) A0 is a continuous vector field whose distributional divergence δ(A0) with respect to the Gaussian measure γd exists, (ii) A0 has Sobolev regularity for some p′>1. Assume for some λ0>0. In case (i), if the pathwise uniqueness of solutions holds, then the push-forward #(Xt)γd admits a density with respect to γd. In particular, if the coefficients are bounded Lipschitz continuous, then Xt leaves the Lebesgue measure Lebd quasi-invariant. In case (ii), we develop a method used by G. Crippa and C. De Lellis for ODE and implemented by X. Zhang for SDE, to establish existence and uniqueness of stochastic flow of maps. 相似文献
9.
In the Sobolev space
, where is a bounded domain in n with a Lipschitzian boundary, for an arbitrarily given
, we construct a basis such that the error of approximation of a function
the Nth partial sum of its expansion with respect to this basis can be estimated in terms of the modulus of smoothness
of order
. 相似文献
10.
This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An example of Hermite interpolants is presented to illustrate the result. 相似文献
11.
A. I. Fedotov 《Mathematical Notes》2007,81(3-4):373-378
We obtain an estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space. It is shown that, under a suitable choice of the sequence of multi-indices, interpolation polynomials converge to the interpolated function and their rate of convergence is of the order of the best approximation of this function. 相似文献
12.
13.
This paper is concerned with the time-periodic solution to the simplified incompressible nematic liquid crystal equation. We prove the existence of the time-periodic solution of this equation with small external forces g1 and g2, satisfying the T-periodic conditions gj(t)=gj(t+T) for j=1,2 in weighted Sobolev spaces. 相似文献
14.
Recently, many new features of Sobolev spaces W k,p ?RN ? were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5]. 相似文献
15.
We study the Cauchy problem of the Ostrovsky equation , with βγ<0. By establishing a bilinear estimate on the anisotropic Bourgain space Xs,ω,b, we prove that the Cauchy problem of this equation is locally well-posed in the anisotropic Sobolev space H(s,ω)(R) for any and some . Using this result and conservation laws of this equation, we also prove that the Cauchy problem of this equation is globally well-posed in H(s,ω)(R) for s?0. 相似文献
16.
A. S. Leonov 《Mathematical Notes》2005,77(3-4):348-363
In this paper, we consider special classes of strongly convex functionals in Sobolev spaces. It is proved that functionals from such classes have the so-called H-property: weak convergence of sequences of arguments and convergence of such sequences with respect to a given functional imply strong convergence.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 378–394.Original Russian Text Copyright © 2005 by A. S. Leonov.This revised version was published online in April 2005 with a corrected issue number. 相似文献
17.
Jun Kawabe 《Proceedings of the American Mathematical Society》2000,128(11):3291-3300
In this paper, we extend a type of Strassen's theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.
18.
Fumihiro Sato 《Proceedings Mathematical Sciences》1994,104(1):99-135
The theory of zeta functions associated with prehomogeneous vector spaces (p.v. for short) provides us a unified approach
to functional equations of a large class of zeta functions. However the general theory does not include zeta functions related
to automorphic forms such as the HeckeL-functions and the standardL-functions of automorphic forms on GL(n), even though they can naturally be considered to be associated with p.v.’s. Our aim is to generalize the theory to zeta
functions whose coefficients involve periods of automorphic forms, which include the zeta functions mentioned above.
In this paper, we generalize the theory to p.v.’s with symmetric structure ofK
ε-type and prove the functional equation of zeta functions attached to automorphic forms with generic infinitesimal character.
In another paper, we have studied the case where automorphic forms are given by matrix coefficients of irreducible unitary
representations of compact groups.
Dedicated to the memory of Professor K G Ramanathan 相似文献
19.
Xiangqing Zhao Cuihua Guo Wancheng Sheng 《Journal of Mathematical Analysis and Applications》2011,382(1):97-109
In this paper we study the Cauchy problem of the non-isotropically perturbed fourth-order nonlinear Schrödinger type equation: ((x1,x2,…,xn)∈Rn, t?0), where a is a real constant, 1?d<n is an integer, g(x,|u|)u is a nonlinear function which behaves like α|u|u for some constant α>0. By using Kato method, we prove that this perturbed fourth-order Schrödinger type equation is locally well-posed with initial data belonging to the non-isotropic Sobolev spaces provided that s1,s2 satisfy the conditions: s1?0, s2?0 for or for with some additional conditions. Furthermore, by using non-isotropic Sobolev inequality and energy method, we obtain some global well-posedness results for initial data belonging to non-isotropic Sobolev spaces . 相似文献
20.
Mostafa Bendahmane Moussa Chrif Said El Manouni 《Mathematical Methods in the Applied Sciences》2010,33(1):49-56
We deal with the existence and uniqueness of weak solutions for a class of strongly nonlinear boundary value problems of higher order with L1 data in anisotropic‐weighted Sobolev spaces of infinite order. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献