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$C_0$-semigroups generated by second order differential operators

Volume 116 / 2016

Gabriela Raluca Mocanu Annales Polonici Mathematici 116 (2016), 57-66 MSC: Primary 47D06; Secondary 47D07, 47F05, 47B65. DOI: 10.4064/ap3737-12-2015 Published online: 3 December 2015

Abstract

Let $W(u)(x)=\frac {1}{2}x^a(1-x)^bu''(x)$ with $a,b\geq 2$. We consider the $C_0$-semigroups generated by this operator on the spaces of continuous functions, respectively square integrable functions. The connection between these semigroups together with suitable approximation processes is studied. Also, some qualitative and quantitative properties are derived.

Authors

  • Gabriela Raluca MocanuAstronomical Institute
    Astronomical Observatory Cluj-Napoca
    Romanian Academy
    15 Cire\c silor St.
    400487 Cluj-Napoca, Romania
    e-mail

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