摘要:

We view Shannon's sampling procedure as a problem of approximation in the spaceS= {s:s(x) = (c* sinc)(x)cεl2}. We show that under suitable conditions on a generating function λ εL2, the approximation problem onto the spaceV= {v:v(x) = (c* λ)(x)cεl2} produces a sampling procedure similar to the classical one. It consists of an optimal prefiltering, a pure jitter-stable sampling, and a postfiltering for the reconstruction. We describe equivalent signal representations using generic, dual, cardinal, and orthogonal basis functions and give the expression of the corresponding filters. We then consider sequences λn, where λndenotes then-fold convolution of λ. They provide a sequence of increasingly regular sampling schemes as the value ofnincreases. We show that the cardinal and orthogonal pre- and postfilters associated with these sequences asymptotically converge to the ideal lowpass filter of Shannon. The theory is illustrated using several eamples.

ISSN:0163-0563    

DOI:10.1080/01630569408816545

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

Let (I, μ) be a given finite measure space. IfXis a Banach space, we setLp(IX) to denote the Banach space ofp-Bochner integrable functions. It is the object of this paper to discuss unicity and proximinality ofLp(IG) inLp(IX), whereGis a closed subspace ofX. Further, we generalize the work of Kroo on unicity in vector-valued function spaces. Some other results are presented.

ISSN:0163-0563    

DOI:10.1080/01630569408816546

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

Letbe a normed linear space,andfbe a proper lower semicontinuous convex function defined onX. The Lipschitz reg-ularization offwith parameter μ is the infimal convolution offwith, defined by. In this article we express, in an arbitrary normed space, the twomost important epigraphical convergence notions for convex functions in terms of the convergence of associated Lipschitz regularizations with respect to classical function theoretic modes of convergence. In the case of slice convergence of epigraphs, the associated mode of convergence for the regularizations is pointwise convergence, whereas for Attouch-Wets convergence of epigraphs, the associated mode of convergence for the regularizations is uniform convergence on bounded subsets ofXL.

ISSN:0163-0563    

DOI:10.1080/01630569408816547

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

The characterization of the monotone interpolation and smoothing splines is considered by means of a general optimization problem on a convex subset of a Hilbert space. The results of Hornung [1] and Utreras [2] about the special form of the monotone cubic splines forq= 2 are extended to a higher dimension: it is shown that ifq= 3 the solutions of the monotone smoothing problem and the monotone interpolation problem are both polynomial splines of degree 5 with a finite number of knots.

ISSN:0163-0563    

DOI:10.1080/01630569408816548

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

In this paper we study a nonconforming finite element method for solving a fourth-order elliptic variational inequality related to the clamped plate bending problem with a displacement obstacle. A convergence result and an optimalO(h)-error estimate for the nonconforming finite element approximation using Morley's triangular element are shown. Finally, a duality iterative algorithm is given, and the convergence of this algorithm is proved

ISSN:0163-0563    

DOI:10.1080/01630569408816549

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

This is a continuation of our previous paper [9] where we established the Carathéodory approximate solution for a stochastic evolution equation with variable delay in Hilbert space of the formwhen the coefficientsfandgwere Lipschitz. In this paper we shall show the same approximate solution for the delay equation but the coefficientsfandgare supposed to be weaker than Lipschitz continuity. The proof of the convergence of the Carathéodory approximation represents an alternative to the procedure for establishing the existence and uniqueness of the solution to the delay equation

ISSN:0163-0563    

DOI:10.1080/01630569408816550

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

The direct computation of critical points of nonlinear equations depending on parameters is considered. For solving the corresponding augmented systems a new projective approach is illustrated.

ISSN:0163-0563    

DOI:10.1080/01630569408816551

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

In this paper we consider a system ofmreal linear equationsAx = b, innunknowns which has a nonnegative solution. Out of these nonnegative solutions we seek the one which is of least norm whenis equipped with a strictly convex norm. We give a globally convergent, implementable, iterative algorithm converging to the above solution. Within each iteration cycle occurs a quadratic program for minimizing, subject toAx = bx> 0, where the sequence (ak) is constructed iteratively. After presenting some duality theorems we prove the convergence of the algorithm. As a special case we test the algorithm for thelp-norms (1 > p > ∞). Numerical results are also included.

ISSN:0163-0563    

DOI:10.1080/01630569408816552

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569408816553

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

The composite materials with quasi-periodic microstructure play an important role in optimal structural design. In this paper we study the torsional rigidity of an ε-perforated material, subjected to a volume constraint. It is proved that for any ε>0 there exist a distribution of the holes which maximizes the torsional rigidity functional. Also, we prove the existence of an optimal control of the material governed by the system obtained by homogenization.The main result is that when ε→0 the torsional rigidity of the optimal ε-perforated material tends to the torsional rigidity of the optimal distribution of the macroscopic material.

ISSN:0163-0563    

DOI:10.1080/01630569408816554

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor