Showing results 21 to 34 of 34
  Biorthogonal wavelets in H-m(R)Bastin, Françoise  ; in Journal Of Fourier Analysis And Applications (1998), 4(6), 749-768 This article is concerned with constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer order. Using techniques of [1] and [2], the results presented here ... [more ▼] This article is concerned with constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer order. Using techniques of [1] and [2], the results presented here generalize to Sobolev spaces some constructions of Cohen et al. [7] and Chui and Wang [5] established in L-2(R). [less ▲] Detailed reference viewed: 13 (3 ULg)A walk in the the theory of wavelets from L^2(R) to H^s(R).Bastin, Françoise ; in Rendiconti del circolo Matematico Di Palermo (2) Suppl (1998), 52(1), 239-252 Detailed reference viewed: 17 (2 ULg)Compactly supported wavelets in Sobolev spaces of integer orderBastin, Françoise ; in Applied & Computational Harmonic Analysis (1997), 4(1), 51-57 We present a construction of regular compactly supported wavelets in any Sobolev space of integer order. It is based on the existence and suitable estimates of filters defined from polynomial equations ... [more ▼] We present a construction of regular compactly supported wavelets in any Sobolev space of integer order. It is based on the existence and suitable estimates of filters defined from polynomial equations. We give an implicit study of these filters and use the results obtained to construct scaling functions leading to multiresolution analysis and wavelets. Their regularity increases linearly with the length of their supports as in the L(2) case. One technical problem is to prove that the intersection of the scaling spaces is reduced to 0. This is solved using sharp estimates of Littlewood-Paley type. (C) 1997 Academic Press, Inc. [less ▲] Detailed reference viewed: 20 (2 ULg)Regular compactly supported wavelets in Sobolev spacesBastin, Françoise ; in Duke Mathematical Journal (1997), 87(3), 481-508 Detailed reference viewed: 22 (0 ULg)Singular Spectrum and functional properies of kernelsBastin, Françoise ; in Functional Analysis, Trier, 1994 (1996) Detailed reference viewed: 6 (0 ULg)A general functional characterization of the microlocal singularitiesBastin, Françoise ; in Journal of Mathematical Sciences, The University of Tokyo (1995), 2(1), 155-164 Detailed reference viewed: 8 (0 ULg)ON THE FUNCTIONAL-CHARACTERIZATION OF THE ANALYTIC WAVE-FRONT SET OF AN HYPERFUNCTIONBastin, Françoise ; in Mathematische Nachrichten (1994), 166 Detailed reference viewed: 17 (5 ULg)DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONSBastin, Françoise in Proceedings Of The Edinburgh Mathematical Society (1992), 35(Part 2), 271-283 In this paper, we prove that if U is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that VBAR congruent-to VBAR and C(X), then the Frechet ... [more ▼] In this paper, we prove that if U is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that VBAR congruent-to VBAR and C(X), then the Frechet space CU(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequence U satisfies condition (H) (cf. e.g.`[1] for the introduction of (H)). As a consequence, the bidual lambda(infinity)(A) of the distinguished Kothe echelon space lambda-0(A) is distinguished if and only if the space lambda-1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Kothe echelon spaces. [less ▲] Detailed reference viewed: 14 (0 ULg) LOCALLY BOUNDED NONCONTINUOUS LINEAR-FORMS ON STRONG DUALS OF NONDISTINGUISHED KOTHE ECHELON SPACESBastin, Françoise ; in Proceedings of the American Mathematical Society (1990), 108(3), 769-774 In this note it is proved that if Al (A) is any nondistinguished Kothe echelon space of order one and K. ,0 (AI (A))' is its strong dual, then there is even a linear form : K - C which is locally bounded ... [more ▼] In this note it is proved that if Al (A) is any nondistinguished Kothe echelon space of order one and K. ,0 (AI (A))' is its strong dual, then there is even a linear form : K - C which is locally bounded (i.e. bounded on the bounded sets) but not continuous. It is also shown that every nondistinguished Kothe echelon space contains a sectional subspace with a particular structure [less ▲] Detailed reference viewed: 11 (2 ULg)Weighted spaces of continuous functionsBastin, Françoise in Bulletin de la Société Royale des Sciences de Liège (1990), 59(1), 3-82 Detailed reference viewed: 29 (0 ULg)On Cartan's A and B theoremsBastin, Françoise ; Schneiders, Jean-Pierre in Bulletin de la Société Royale des Sciences de Liège (1990), 59(3-4), 269-288 Detailed reference viewed: 19 (7 ULg)ON BORNOLOGICAL CV-BAR(X) SPACESBastin, Françoise in Archiv Der Mathematik (1989), 53(4), 394-398 Detailed reference viewed: 4 (1 ULg)A criterion for CV(X) to be quasinormableBastin, Françoise ; in Results in Mathematics (1988), 14(3-4), 223-230 Detailed reference viewed: 8 (0 ULg)A weighted characterization of the locally compact and \sigma compact spacesBastin, Françoise ; Schmets, Jean in Bulletin de la Société Royale des Sciences de Liège (1988), 57(1-2), 73-78 Detailed reference viewed: 15 (6 ULg)
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