Showing papers in "Revista Matematica Complutense in 1988"
TL;DR: In this paper, the authors give a constructive proob that given a bounded Iunction on a rectangle R, the minimum of the following bunctional is achieved: E(u,B) = IIu − gIV~(R> + 1(B), where B is a finite set of C' curves lii R and u is locally constant in R −B. Following ideas ob Mumbord and Shah, their proob suggests a method for transborming an image into a cartoon.
Abstract: Wc give a constructive proob that given a bounded Iunction on a rectangle R, the minimum of the following bunctional is achieved: E(u,B)= IIu — gIV~(R> +1(B), where B is a finite set ob C' curves lii R and u is locally constant in R —B. In image processing, g can be interpreted as an image (g(x,y) is the grey level a! (x,y)) and the curves ob B as the contours of the image, u representing the mean value inside each contour. Following ideas ob Mumbord and Shah, our proob suggests a method br transborming an image into a cartoon.
66 citations
TL;DR: Sorne results about the density of continuous maps from Q, a baunded regular domain of pN to 5M in the Sobolev classes W 3~(Q, Sa) are given in this paper.
Abstract: Sorne results are given about ihe density ofcontinuous maps from Q, a baunded regular domain of pN to 5M in the Sobolev classes W 3~(Q, Sa).
25 citations
10 citations
TL;DR: In this paper, it was shown that if X is a separable Banach space, then the topological dual space of X is the algebra of real analytic functions on X and every character 4 of A is a point evaluation at a given point of X.
Abstract: Lei X be a completely regular Hausdorff space and C(X) the algebra of ali continuous <-valued functions on X (1K = IR o C). If AE C(X) is a subalgebra, in (4) can be found conditions on A under whicls cadi character ofA, i.e., each non-zero 1K-linear multiplicative funclional 4xA—* 1K, is given by a point evaluation al sorne point of X. In ibis paper we preseni a «Michael» type theorem for the particular case in which X is a real Banach space. As consequence it is showed thai if E is a separable Banach space or Ei sthe topological dual space of a separable Banach space aud A is the algebra of ah real analytic or the algebra of ali real Cm.functions, ni = 0, 1 oD, on E, then every character 4 of A is a point evaluation at sorne poini of E. Let E be a real Hanach space with topological dual E' and let C(E) be the algebra of ali continuous IR-valued bunctions on E. Let ll(~~J)={a=(a»)eIRN~ o, ~ a t,~09}. n1
6 citations
TL;DR: In this paper, several conditions are given under which L1, embeds as a complemented subspace of a Banach space E if and only if it embeds in an Orlicz space of E-valued functions.
Abstract: Several conditions are given under which L1, embeds as a complemented subspace of a Banach space E if it embeds as a complemented sudspace of an Orlicz space of E-valued functions. Previous results in (7) and (1) are extended in this way.
4 citations
1 citations
TL;DR: In this paper, the authors introduce the concept of co-solution of an algebraic equation of the type X 2 +A,X+A 0 = 0, that allows us to obtain a metliod of the variation of the pararneters for the matrix case and to find uniqueness conditions for solutions of boundary value problems.
Abstract: In this paper we show that in an analogous way to ite scalar case, the general solution oba non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions ob certain matrices related to ite corresponding characteristic algebraic matrix equation. Wc introduce dic concept of co-solution ob an algebraic equation of the type X 2 +A ,X+A 0 = 0, that allows us to obtain a metliod of the variation ob tlie pararneters for the matrix case and furiher to fiad existence, uniqueness conditions for solutions of boundary value problems. Ihese conditions are of algebrale type, involving the Penrose-Moore pseudoinverse of a matrix related to the problern. A computable closed form for solutions of dic problem is given.
1 citations
TL;DR: The main result of as mentioned in this paper is that a separate Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence of nested, closed, finite condimensional subspaces with null intersections.
Abstract: The main result of this paper is the following: a separate Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence of nested, closed, finite condimensional subspaces with null intersections.
1 citations
TL;DR: In this article, the robustness of the estimator, if the nonresponse mechanism is not fixed by simple random sampling, is characterized when the correct approach is related with the beed of subsampling the non-response stratum.
Abstract: Singh-Singh (1979) considered the nonresponses as generated by a mechanism which is equivalent to simple random sampling (srs). They proposed an estimator under the hypothesis associated. It is unbiased and its variance is a function of an unknown parameter. An approximate expresion of its variance is presented in this paper. The robustness of the estimator, if the nonresponse mechanism is not fixed by srs, is characterized when the correct approach is related with the beed of subsampling the nonresponse stratum.