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Pseudodifferential operators on non-quasianalytic classes of Beurling type

C. FernándezA. GalbisD. Jornet — 2005

Studia Mathematica

We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class ( ω ) ' is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class ( ω ) ' . We also...

Fuzzy systems and neural networks XML schemas for Soft Computing.

Adolfo Rodríguez de SotoConrado Andreu CapdevilaE. C. Fernández — 2003

Mathware and Soft Computing

This article presents an XML[2] based language for the specification of objects in the Soft Computing area. The design promotes reuse and takes a compositional approach in which more complex constructs are built from simpler ones; it is also independent of implementation details as the definition of the language only states the expected behaviour of every possible implementation. Here the basic structures for the specification of concepts in the Fuzzy Logic area are described and a simple construct...

BMO-scale of distribution on n

René Erlín CastilloJulio C. Ramos Fernández — 2008

Czechoslovak Mathematical Journal

Let S ' be the class of tempered distributions. For f S ' we denote by J - α f the Bessel potential of f of order α . We prove that if J - α f B M O , then for any λ ( 0 , 1 ) , J - α ( f ) λ B M O , where ( f ) λ = λ - n f ( φ ( λ - 1 · ) ) , φ S . Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order α > 0 belongs to the V M O space.

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