Total Positivity: an application to positive linear operators and to their limiting semigroups

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Antonio Attalienti
Ioan Raşa

Abstract

Some shape-preserving properties of positive linear operators, involving higher order convexity and Lipschitz classes, are investigated from the point of view of weak Tchebycheff systems and total positivity in the sense of Karlin [8]. The same properties are shown to be fulfilled by the strongly continuous semigroup \((T(t))_{t\geq 0}\), if any, generated by the iterates of the relevant operators, in the spirit of Altomare's theory.
Keywords
weak Tchebycheff systems, total positivity, positive linear operators, strongly continuous semigroups

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How to Cite
Attalienti, A., & Raşa, I. (2007). Total Positivity: an application to positive linear operators and to their limiting semigroups. Rev. Anal. Numér. Théor. Approx., 36(1), 51-66. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no1-art5
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