Degenerate evolution problems and Beta-type operators
Attalienti, Antonio ; Campiti, Michele
Studia Mathematica, Tome 141 (2000), p. 117-139 / Harvested from The Polish Digital Mathematics Library
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The present paper is concerned with the study of the differential operator Au(x):=α(x)u”(x)+β(x)u’(x) in the space C([0,1)] and of its adjoint Bv(x):=((αv)’(x)-β(x)v(x))’ in the space L1(0,1), where α(x):=x(1-x)/2 (0≤x≤1). A careful analysis of their main properties is carried out in view of some generation results available in [6, 12, 20] and [25]. In addition, we introduce and study two different kinds of Beta-type operators as a generalization of similar operators defined in [18]. Among the corresponding approximation results, we show how they can be used in order to represent explicitly the solutions of the Cauchy problems associated with the operators A and Ã, where à is equal to B up to a suitable bounded additive perturbation.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216758 
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     title = {Degenerate evolution problems and Beta-type operators},
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     year = {2000},
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Attalienti, Antonio; Campiti, Michele. Degenerate evolution problems and Beta-type operators. Studia Mathematica, Tome 141 (2000) pp. 117-139. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv140i2p117bwm/

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