共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper first presents a condensed state of art on multiresolution analysis using polyharmonic splines: definition and main properties of polyharmonic splines, construction of B-splines and wavelets, decomposition and reconstruction filters; properties of the so-obtained operators, convergence result and applications are given. Second this paper presents some new results on this topic: scattered data wavelet, new polyharmonic scaling functions and associated filters. Fourier transform is of extensive use to derive the tools of the various multiresolution analysis. 相似文献
2.
Analytical particular solutions of augmented polyharmonic spline associated with Mindlin plate model
Chia‐Cheng Tsai Edward Ming‐Yang Wu 《Numerical Methods for Partial Differential Equations》2012,28(6):1778-1793
Analytical particular solutions of the augmented polyharmonic spline (APS) associated with the polyharmonic and poly‐Helmholtz operators and their products were derived by Tsai et al. (Eng Anal Bound Elem 33 (2009), 514). In addition, it has been mentioned that the particular solution associated with a coupled system of partial differential equations (PDEs) can be derived from the prescribed solutions by using the Hörmander operator decomposition technique. In this article, this derivation procedure is demonstrated via Mindlin thick‐plate problems, which are governed by a coupled system of three second‐order PDEs. Analytical particular solutions of displacements, shear forces, and bending or twisting moments corresponding to the polyharmonic spline and monomials are all explicitly derived. These particular solutions are validated using numerical examples. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
3.
The purpose of this paper is to provide multiresolution analysis, stationary subdivision and pre-wavelet decomposition onL
2(R
d
) based on a general class of functions which includes polyharmonic B-splines.The work of this author has been partially supported by a DARPA grant.The work of this author has been partially supported by Fondo Nacional de Ciencia y Technologia under Grant 880/89. 相似文献
4.
A Dirichlet problem for polyharmonic functions 总被引:1,自引:0,他引:1
In this article, the Dirichlet problem of polyharmonic functions is considered. As well the explicit expression of the unique
solution to the simple Dirichlet problem for polyharmonic functions is obtained by using the decomposition of polyharmonic
functions and turning the problem into an equivalent Riemann boundary value problem for polyanalytic functions, as the approach
to find the kernel functions of the solution for the general Dirichlet problem is given.
Project supported by NNSF of China. 相似文献
5.
In this paper, we establish a decomposition theorem for polyharmonic functions and consider its applications to some Dirichlet problems in the unit disc. By the decomposition, we get the unique solution of the Dirichlet problem for polyharmonic functions (PHD problem) and give a unified expression for a class of kernel functions associated with the solution in the case of the unit disc introduced by Begehr, Du and Wang. In addition, we also discuss some quasi-Dirichlet problems for homogeneous mixed-partial differential equations of higher order. It is worthy to note that the decomposition theorem in the present paper is a natural extension of the Goursat decomposition theorem for biharmonic functions. 相似文献
6.
Liu Yongping 《应用数学学报(英文版)》1998,14(2):157-164
The remainders and the convergence of cardinal polyharmonic spline interpolation are studied, and the asymptotic behavior
of the best approximation by polyharmonic spline and the averageK-width of some class of smooth functions defined on the Euclidean spaceR
n are determined.
This project is supported by the National Natural Science Foundation of China (No. 19671012) and by the Doctoral Programme
Foundation of Institution of Higher Education of Country Education Committee of China. 相似文献
7.
Filippo Gazzola Hans-Christoph Grunau 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(1):35-44
Pucci and Serrin [21] conjecture that certain space dimensions behave 'critically' in a semilinear polyharmonic eigenvalue
problem. Up to now only a considerably weakened version of this conjecture could be shown. We prove that exactly in these
dimensions an embedding inequality for higher order Sobolev spaces on bounded domains with an optimal embedding constant may
be improved by adding a 'linear' remainder term, thereby giving further evidence to the conjecture of Pucci and Serrin from
a functional analytic point of view. Thanks to Brezis-Lieb [5] this result is already known for the space in dimension n=3; we extend it to the spaces (K>1) in the 'presumably' critical dimensions. Crucial tools are positivity results and a decomposition method with respect
to dual cones.
Received June 1999 相似文献
8.
This paper introduces a domain decomposition preconditioner for
elliptic equations with rough coefficients. The coarse space of the
domain decomposition method is constructed via the so-called rough
polyharmonic splines (RPS for short). As an approximation space of
the elliptic problem, RPS is known to recover the quasi-optimal
convergence rate and attain the quasi-optimal localization property.
The authors lay out the formulation of the RPS based domain
decomposition preconditioner, and numerically verify the performance
boost of this method through several examples. 相似文献
9.
P. Lesky 《Mathematical Methods in the Applied Sciences》1990,12(4):275-291
Consider the polyharmonic wave equation ?u + (? Δ)mu = f in ?n × (0, ∞) with time-independent right-hand side. We study the asymptotic behaviour of u ( x , t) as t → ∞ and show that u( x , t) either converges or increases with order tα or In t as t → ∞. In the first case we study the limit $ u_0 \left({\bf x} \right) \colone \mathop {\lim }\limits_{t \to \infty } \,u\left({{\bf x},t} \right) $ and give a uniqueness condition that characterizes u0 among the solutions of the polyharmonic equation ( ? Δ)mu = f in ?n. Furthermore we prove in the case 2m ? n that the polyharmonic equation has a solution satisfying the uniqueness condition if and only if f is orthogonal to certain solutions of the homogeneous polyharmonic equation. 相似文献
10.
ABSTRACTThe classical Doob–Meyer decomposition and its uniform version the optional decomposition are stated on probability spaces with filtrations satisfying the usual conditions. However, the comprehensive needs of filtering theory and mathematical finance call for their generalizations to more abstract spaces without such technical restrictions. The main result of this paper states that there exists a uniform Doob–Meyer decomposition of optional supermartingales on unusual probability spaces. This paper also demonstrates how this decomposition works in the construction of optimal filters in the very general setting of the filtering problem for optional semimartingales. Finally, the application of these optimal filters of optional semimartingales to mathematical finance is presented. 相似文献
11.
REN Guangbin Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2005,48(Z1)
Let Ωbe a G-invariant convex domain in RN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ωwhich are Dunkl polyharmonic, i.e. (△h)nf =0 for some integer n. Here △h=∑j=1N Dj2 is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G, where kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form f(x)=f0(x) |x|2f1(x) … |x|2(n-1)fn-1(x),(?)x∈Ω, where fj are Dunkl harmonic functions, i.e. △hfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition. 相似文献
12.
By using a special decomposition of the fundamental solution, we construct a new representation of the Green function of the
Dirichlet problem for the polyharmonic equation in a ball. 相似文献
13.
On Priestley Spaces of Lattice-Ordered Algebraic Structures 总被引:1,自引:0,他引:1
The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed. 相似文献
14.
Factoring wavelet transforms into lifting steps 总被引:236,自引:0,他引:236
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with
finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are
also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet
or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed
by the formulaSL(n;R[z, z−1])=E(n;R[z, z−1])); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation,
building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering.
This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the
biorthogonal, i.e., non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces
the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining
a wavelet-like transform that maps integers to integers.
Research Tutorial
Acknowledgements and Notes. Page 264. 相似文献
15.
16.
Fengping Yao 《Archiv der Mathematik》2008,90(5):429-439
In this paper we generalize classical L
p
estimates to Orlicz spaces for the parabolic polyharmonic equations. Our argument is based on the iteration-covering procedure.
Received: 10 September 2007 相似文献
17.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
18.
H. Render 《Archiv der Mathematik》2008,91(2):136-144
The reproducing kernel of the space of all homogeneous polynomials of degree k and polyharmonic order m is computed explicitly, solving a question of A. Fryant and M. K. Vemuri.
Received: 17 May 2007, Revised: 27 March 2008 相似文献
19.
Let Ω be a G-invariant convex domain in ℝN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ω which are Dunkl polyharmonic, i.e. (Δh)nf = 0 for some integer n. Here333-01is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G,
$$\mathcal{D}_j f(x) = \frac{\partial }{{\partial x_j }}f(x) + \sum\limits_{v \in R_ + } {\kappa _v \frac{{f(x) - f(\sigma _v x)}}{{\left\langle {x,v} \right\rangle }}} v_j ,$$where Kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form
$$f(x) = f_0 (x) + \left| x \right|^2 f_1 (x) + \cdots + \left| x \right|^{2(n - 1)} f_{n - 1} (x), \forall x \in \Omega ,$$where fj are Dunkl harmonic functions, i.e. Δhfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition.
相似文献20.
Zuchi Chen 《应用数学学报(英文版)》1987,3(1):50-57
In this paper we consider the bounds of the eigenvalues for a class of polyharmonic operators and obtain the bounds for (n+1)th eigenvalue interm of the firstn eigenvalues. Those estimates do not depend on the domain in which the problem is considered. 相似文献