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81.
Regularity of multiwavelets 总被引:7,自引:0,他引:7
The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields. 相似文献
82.
G. J. Groenewald M. A. Petersen Y. Zucker 《Integral Equations and Operator Theory》1997,28(4):466-491
For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices. 相似文献
83.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
84.
Kehe Zhu 《Integral Equations and Operator Theory》1998,31(3):371-387
The paper deals with two closely related questions about the Bergman space of the unit disk. First, we investigate a special class of invariant subspaces of the Bergman space, namely, invariant subspaces induced by certain Hankel operators. We show that such spaces always have the co-dimension 1 or 2 property; and we determine exactly when such a space has the co-dimension 1 property. Second, we introduce the notion of inner spaces in the Bergman space and give several characterizations of when an inner space is maximal.Research supported by the National Science Foundation 相似文献
85.
An effective residual interaction between particles and holes for shell model calculations around 208Pb, derived from the interaction between free nucleons, is compared with the measured properties of proton-hole neutron states
in 208Tl and the interaction between proton holes is adjusted to newly measured level energies in 206Hg. These interaction elements are particularly relevant for neutron-rich nuclei. The adjustment of two mixing elements reproduces
the known γ-decay data in 208Tl.
Received: 2 April 2002 / Accepted: 2 May 2002 相似文献
86.
87.
A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ
d
withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections
with statistical mechanics. Of course, polygons on ℤ
d
are defined up to a translation, and the relevant statistic is their perimeter.
A SAP on ℤ
d
is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing
it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher
dimension.
We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's
result, which explains combinatorially the form of the generating function. We then compute the generating function for convex
SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However,
our method suggests that the generating function for convex SAPs on ℤ
d
is always a quotient ofdifferentiably finite power series. 相似文献
88.
89.
Sans résumé
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90.
Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4]. 相似文献