References of "Bastin, Françoise"
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See detailCoherent states, wavelets and applications G24 - LLN
Antoine, J. P.; Bastin, Françoise ULg; De Mol, C. et al

in Group 24 : Physical and Mathematical Aspects of Symmetries (2003)

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See detailDeficient splines wavelets
Bastin, Françoise ULg; Laubin, P.; Kerner, R. et al

in Group 24 : Physical And Mathematical Aspects Of Symmetries (2003), 173

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See detailA general recurrence relation between the moments of a scaling function
Bastin, Françoise ULg; Nicolay, Samuel ULg

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 ▲]

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See detailDeficient splines wavelets
Bastin, Françoise ULg; Laubin, P.

in Group 24 : Physical and Mathematical Aspects of Symmetries (2003)

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See detailSpline wavelets in periodic Sobolev spaces and application to high order collocation methods
Bastin, Françoise ULg; Boigelot, Christine; Laubin, Pascal

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 ▲]

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See detailA general recurrence relation between the moments of a scaling function
Bastin, Françoise ULg; Nicolay, Samuel ULg

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 ▲]

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See detailQuintic deficient spline wavelets
Bastin, Françoise ULg; Laubin, Pascal

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.

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See detailConstructions and applications of wavelets in Sobolev spaces
Bastin, Françoise ULg

in Revista Ciencias Matematicas (2000), 18(2), 145-177

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See detailBiorthogonal wavelets in H-m(R)
Bastin, Françoise ULg; Boigelot, Christine

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 ▲]

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See detailA walk in the the theory of wavelets from L^2(R) to H^s(R).
Bastin, Françoise ULg; Laubin, Pascal

in Rendiconti del circolo Matematico Di Palermo (2) Suppl (1998), 52(1), 239-252

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See detailCompactly supported wavelets in Sobolev spaces of integer order
Bastin, Françoise ULg; Laubin, P.

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 ▲]

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See detailRegular compactly supported wavelets in Sobolev spaces
Bastin, Françoise ULg; Laubin, P.

in Duke Mathematical Journal (1997), 87(3), 481-508

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See detailSingular Spectrum and functional properies of kernels
Bastin, Françoise ULg; Laubin, Pascal

in Functional Analysis, Trier, 1994 (1996)

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See detailA general functional characterization of the microlocal singularities
Bastin, Françoise ULg; Laubin, Pascal

in Journal of Mathematical Sciences, The University of Tokyo (1995), 2(1), 155-164

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See detailON THE FUNCTIONAL-CHARACTERIZATION OF THE ANALYTIC WAVE-FRONT SET OF AN HYPERFUNCTION
Bastin, Françoise ULg; LAUBIN, P.

in Mathematische Nachrichten (1994), 166

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See detailDISTINGUISHEDNESS OF WEIGHTED FRECHET SPACES OF CONTINUOUS-FUNCTIONS
Bastin, Françoise ULg

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 ▲]

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See detailLOCALLY BOUNDED NONCONTINUOUS LINEAR-FORMS ON STRONG DUALS OF NONDISTINGUISHED KOTHE ECHELON SPACES
Bastin, Françoise ULg; Bonet, Jose

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 ▲]

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See detailWeighted spaces of continuous functions
Bastin, Françoise ULg

in Bulletin de la Société Royale des Sciences de Liège (1990), 59(1), 3-82

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See detailOn Cartan's A and B theorems
Bastin, Françoise ULg; Schneiders, Jean-Pierre ULg

in Bulletin de la Société Royale des Sciences de Liège (1990), 59(3-4), 269-288

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See detailON BORNOLOGICAL CV-BAR(X) SPACES
Bastin, Françoise ULg

in Archiv Der Mathematik (1989), 53(4), 394-398

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