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On some PDEs involving homogeneous operators. Spectral analysis, semigroups and Hardy inequalities Rodríguez Bernal, Aníbal Cholewa, Jan W. 517.98 Homogeneity Semigroups of linear operators Spectrum Fractional diffusion Resolvent Numerical range Matemáticas (Matemáticas) Análisis funcional y teoría de operadores 12 Matemáticas 1202 Análisis y Análisis Funcional Motivated by the analysis of homogeneous operators and semigroups in [10], in this paper we perform an spectral analysis of homogeneous operators and give simple characterization of generators of homoge- neous semigroups and of homogeneous sectorial operators. We also analyse homogeneous perturbations of homogeneous operators and semigroups. We use these results to study some parabolic PDEs involving homogeneous operators including some fractional diffusion problems. We show a deep connection of these results with some Gagliardo–Nirenberg and Hardy type inequalities. Ministerio de Economía, Comercio y Empresa (España) Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-11-17T12:30:21Z 2023-11-17T12:30:21Z 2022 journal article CVoR https://hdl.handle.net/20.500.14352/88793 0022-0396 10.1016/j.jde.2022.01.029 eng MTM2016-75465 PID2019-103860GB-I00 Cholewa, J. W., & Rodriguez-Bernal, A. (2022). On some PDEs involving homogeneous operators. Spectral analysis, semigroups and Hardy inequalities. Journal Of Differential Equations, 315, 1-56. https://doi.org/10.1016/j.jde.2022.01.029 Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ restricted access application/pdf Elsevier