Rodríguez Bernal, AníbalCholewa, Jan W.2023-11-172023-11-172022Cholewa, 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.2022.01.0290022-039610.1016/j.jde.2022.01.029https://hdl.handle.net/20.500.14352/88793Motivated 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1016/j.jde.2022.01.029http://www.elsevier.com/locate/jderestricted access517.98HomogeneitySemigroups of linear operatorsSpectrumFractional diffusionResolventNumerical rangeMatemáticas (Matemáticas)Análisis funcional y teoría de operadores12 Matemáticas1202 Análisis y Análisis Funcional