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    • Curaduría Digital: Segundo Semestre 2016-17
    • Tarea metadatos I
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    Fractional gaussian estimates and holomorphy of semigroups

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    Thesis doctoral Fabian Seones Correa (409.1Kb)
    Date
    2019-10
    Author
    Seoanes Correa, Fabian
    Keyantuo, Valentín (Advisor)
    Warma, Mahamadi (Advisor)
    El Mennaoui, Omar (Reader)
    Li, Liangquin (Reader)
    Shan, Lin (Reader)
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    Abstract
    Let Ω ⊂ RN be an arbitrary open set and denote by (e−t(−∆)sRN )t≥0 (where 0 < s < 1) the semigroup on L 2 (R N ) generated by the fractional Laplace operator. In the first part of the thesis we show that if T is a self-adjoint semigroup on L 2(Ω) satisfying a fractional Gaussian estimate in the sense that |T(t)f| ≤ Me−bt(−∆)s RN |f|,0 ≤ t ≤ 1, f ∈ L2(Ω), for some constants M ≥ 1 and b ≥ 0, then T defines a bounded holomorphic semigroup of angle π2 that interpolates on L p (Ω), 1 ≤ p < ∞. Additionally, if T0 is a semigroup on C0(Ω) such that T0(t)f = T(t)f for all f ∈ C0(Ω) ∩ L 2(Ω), we prove that the same result also holds on the space C0(Ω). If Ω is bounded then the same conclusion holds for C(Ω). Also, we apply the above results to the realization of fractional order operators with the exterior Dirichlet conditions.
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    https://dspacetestupr.cloudapp.net/handle/11721/10613
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