References of "Journal of Mathematical Analysis & Applications"
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See detailGeneric results in classes of ultradifferentiable functions
Esser, Céline ULg

in Journal of Mathematical Analysis & Applications (2014), 413(1), 378391

Let E be a Denjoy Carleman class of ultradifferentiable functions of Beurling type on the real line that strictly contains another class F of Roumieu type. We show that the set S of functions in E that ... [more ▼]

Let E be a Denjoy Carleman class of ultradifferentiable functions of Beurling type on the real line that strictly contains another class F of Roumieu type. We show that the set S of functions in E that are nowhere in the class F is large in the topological sense (it is residual), in the measure theoretic sense (it is prevalent), and that SU{0} contains an infinite dimensional linear subspace (it is lineable). Consequences for the Gevrey classes are given. Similar results are also obtained for classes of ultradifferentiable functions defined imposing conditions on the Fourier Laplace transform of the function. [less ▲]

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See detailMeasuring the interactions among variables of functions over the unit hypercube
Marichal, Jean-Luc; Mathonet, Pierre ULg

in Journal of Mathematical Analysis & Applications (2011), 380

By considering a least squares approximation of a given square integrable function f: [0,1]^n\to\R by a multilinear polynomial of a specified degree, we define an index which measures the overall ... [more ▼]

By considering a least squares approximation of a given square integrable function f: [0,1]^n\to\R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f, as an expected value of the derivatives of f. Finally, we discuss a few applications of the interaction index in aggregation function theory. [less ▲]

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See detailAdvanced topology on the multiscale sequence spaces S-nu
Aubry, Jean-Marie ULg; Bastin, Françoise ULg

in Journal of Mathematical Analysis & Applications (2009), 350(2), 439-454

We put-sue the Study of the multiscale spaces S-v introduced by Jaffard in the context of multifractal analysis. We give the necessary and Sufficient condition for S-v to be locally p-convex, and exhibit ... [more ▼]

We put-sue the Study of the multiscale spaces S-v introduced by Jaffard in the context of multifractal analysis. We give the necessary and Sufficient condition for S-v to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of S-v is identified to another sequence space depending on v, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces. (C) 2007 Elsevier Inc. All rights reserved. [less ▲]

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