Taiwanese Journal of Mathematics

ON THE C0-SEMIGROUPS GENERATED BY SECOND ORDER DIFFERENTIAL OPERATORS ON THE REAL LINE

Francesco Altomar and Sabina Milella

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Abstract

In this paper we deal with special classes of second order elliptic differential operators on the real line. We show that these operators are generators of positive $C_{0}$-semigroups on weighted spaces of continuous functions and we represent them as limits of iterates of integral-type operators. By means of such representation, some qualitative properties of the semigroups are stated.

Article information

Source
Taiwanese J. Math., Volume 13, Number 1 (2009), 25-46.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405271

Digital Object Identifier
doi:10.11650/twjm/1500405271

Mathematical Reviews number (MathSciNet)
MR2489306

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 35A35: Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx} 35K15: Initial value problems for second-order parabolic equations 41A36: Approximation by positive operators

Keywords
positive semigroup parabolic equation integral operator weighted continuous function space approximation by positive operators

Citation

Altomar, Francesco; Milella, Sabina. ON THE C0-SEMIGROUPS GENERATED BY SECOND ORDER DIFFERENTIAL OPERATORS ON THE REAL LINE. Taiwanese J. Math. 13 (2009), no. 1, 25--46. doi:10.11650/twjm/1500405271. https://projecteuclid.org/euclid.twjm/1500405271


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