Browse ORBi by ORBi project

- Background
- Content
- Benefits and challenges
- Legal aspects
- Functions and services
- Team
- Help and tutorials

A note on moments of scaling functions Bastin, Françoise ; Nicolay, Samuel in Rocky Mountain Journal of Mathematics (2004), 34(4, Winter), 1197-1206 In this note we give a proof of a reproducing formula for polynomials using natural decay hypothesis. This leads to a new exact formula for computation of moments of even order. Detailed reference viewed: 39 (15 ULg)Coherent states, wavelets and applications G24 - LLN ; Bastin, Françoise ; et al in Group 24 : Physical and Mathematical Aspects of Symmetries (2003) Detailed reference viewed: 16 (1 ULg)Deficient splines wavelets Bastin, Françoise ; ; et al in Group 24 : Physical And Mathematical Aspects Of Symmetries (2003), 173 Detailed reference viewed: 20 (2 ULg)A general recurrence relation between the moments of a scaling function Bastin, Françoise ; Nicolay, Samuel in Group 24 : Physical and Mathematical Aspects of Symmetries (2003) Under natural and weak hypotheses, we prove a reproducing formula for polynomials. Then we obtain a new recurrence relation between the moments of a scaling function and a new exact formula for the ... [more ▼] Under natural and weak hypotheses, we prove a reproducing formula for polynomials. Then we obtain a new recurrence relation between the moments of a scaling function and a new exact formula for the computation of moments of even order. [less ▲] Detailed reference viewed: 35 (10 ULg)Deficient splines wavelets Bastin, Françoise ; in Group 24 : Physical and Mathematical Aspects of Symmetries (2003) Detailed reference viewed: 26 (12 ULg)Spline wavelets in periodic Sobolev spaces and application to high order collocation methods Bastin, Françoise ; ; in Revista de la Union Matematica Argentina (2003), 44(1), 53-74 In this paper, we present a particular family of spline wavelets constructed from the Chui-Wang Riesz basis of $L^2(\mathbb{R})$. The construction is explicit, allowing the study of specific functional ... [more ▼] In this paper, we present a particular family of spline wavelets constructed from the Chui-Wang Riesz basis of $L^2(\mathbb{R})$. The construction is explicit, allowing the study of specific functional properties and rather easy handling in numerical computations. This family constitutes a Riesz hierarchical basis in periodic Sobolev spaces. We also present a necessary and sufficient condition of strong ellipticity for pseudodifferential operators obtained with respect to these splines. It uses a new expression for the numerical symbol of the boundary integral operators. This expression allows us to use efficiently collocation methods with different meshes and splines. [less ▲] Detailed reference viewed: 67 (7 ULg)A general recurrence relation between the moments of a scaling function Bastin, Françoise ; Nicolay, Samuel in Group 24 : Physical And Mathematical Aspects Of Symmetries (2003), 173 Under natural and weak hypotheses, we prove a reproducing formula for polynomials. Then we obtain a new recurrence relation between the moments of a scaling function and a new exact formula for the ... [more ▼] Under natural and weak hypotheses, we prove a reproducing formula for polynomials. Then we obtain a new recurrence relation between the moments of a scaling function and a new exact formula for the computation of moments of even order. [less ▲] Detailed reference viewed: 30 (10 ULg)Quintic deficient spline wavelets Bastin, Françoise ; in Bulletin de la Société Royale des Sciences de Liège (2002), 71(3), 121-144 We show explicitely how to construct scaling functions and wavelets using quintic deficient splines with compact support and symmetry properties. Detailed reference viewed: 35 (5 ULg)Constructions and applications of wavelets in Sobolev spaces Bastin, Françoise in Revista Ciencias Matematicas (2000), 18(2), 145-177 Detailed reference viewed: 33 (5 ULg)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: 39 (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: 27 (3 ULg)Compactly supported wavelets in Sobolev spaces of integer order Bastin, 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: 49 (7 ULg)Regular compactly supported wavelets in Sobolev spaces Bastin, Françoise ; in Duke Mathematical Journal (1997), 87(3), 481-508 Detailed reference viewed: 68 (1 ULg)Singular Spectrum and functional properies of kernels Bastin, Françoise ; in Functional Analysis, Trier, 1994 (1996) Detailed reference viewed: 9 (0 ULg)A general functional characterization of the microlocal singularities Bastin, Françoise ; in Journal of Mathematical Sciences, The University of Tokyo (1995), 2(1), 155-164 Detailed reference viewed: 11 (1 ULg)ON THE FUNCTIONAL-CHARACTERIZATION OF THE ANALYTIC WAVE-FRONT SET OF AN HYPERFUNCTION Bastin, Françoise ; in Mathematische Nachrichten (1994), 166 Detailed reference viewed: 21 (6 ULg)DISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS Bastin, 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: 20 (1 ULg)LOCALLY BOUNDED NONCONTINUOUS LINEAR-FORMS ON STRONG DUALS OF NONDISTINGUISHED KOTHE ECHELON SPACES Bastin, 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: 15 (2 ULg)Weighted spaces of continuous functions Bastin, Françoise in Bulletin de la Société Royale des Sciences de Liège (1990), 59(1), 3-82 Detailed reference viewed: 39 (0 ULg)On Cartan's A and B theorems Bastin, Françoise ; Schneiders, Jean-Pierre in Bulletin de la Société Royale des Sciences de Liège (1990), 59(3-4), 269-288 Detailed reference viewed: 28 (9 ULg) |
||