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ArticleOriginal scientific text

Title

Degenerate evolution problems and Beta-type operators

Authors 1, 2

Affiliations

  1. Department of Economic Sciences, University of Bari, Via C. Rosalba, 53 70124 Bari, Italy
  2. Department of Mathematics, Polytechnic of Bari, Via E. Orabona, 4 70125 Bari, Italy

Abstract

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.

Keywords

ENG
approximation process, C0-semigroups of contractions, Beta-type operators, differential operators

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Studia Mathematica
2000/140/2
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Pages:
117-139
Main language of publication
English
Received
1999-01-19
Accepted
2000-02-04
Published
2000
Exact and natural sciences