Degenerate evolution problems and Beta-type operators

Antonio Attalienti; Michele Campiti

Studia Mathematica (2000)

  • Volume: 140, Issue: 2, page 117-139
  • ISSN: 0039-3223

Abstract

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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 L 1 ( 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.

How to cite

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Attalienti, Antonio, and Campiti, Michele. "Degenerate evolution problems and Beta-type operators." Studia Mathematica 140.2 (2000): 117-139. <http://eudml.org/doc/216758>.

@article{Attalienti2000,
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 $L^1(0,1)$, 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.},
author = {Attalienti, Antonio, Campiti, Michele},
journal = {Studia Mathematica},
keywords = {approximation process; $C_0$-semigroups of contractions; Beta-type operators; differential operators; -semigroups of contractions; beta type operators},
language = {eng},
number = {2},
pages = {117-139},
title = {Degenerate evolution problems and Beta-type operators},
url = {http://eudml.org/doc/216758},
volume = {140},
year = {2000},
}

TY - JOUR
AU - Attalienti, Antonio
AU - Campiti, Michele
TI - Degenerate evolution problems and Beta-type operators
JO - Studia Mathematica
PY - 2000
VL - 140
IS - 2
SP - 117
EP - 139
AB - 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 $L^1(0,1)$, 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.
LA - eng
KW - approximation process; $C_0$-semigroups of contractions; Beta-type operators; differential operators; -semigroups of contractions; beta type operators
UR - http://eudml.org/doc/216758
ER -

References

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