A Landau-Kolmogorov inequality for generators of families of bounded operators |
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| Authors: | Carlos Lizama Pedro J. Miana |
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| Affiliation: | a Universidad de Santiago de Chile, Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Casilla 307-Correo 2, Santiago, Chile
b Universidad de Zaragoza, Departamento de Matemáticas & I.U.M.A., 50.009, Zaragoza, Spain |
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| Abstract: | A Landau-Kolmogorov type inequality for generators of a wide class of strongly continuous families of bounded and linear operators defined on a Banach space is shown. Our approach allows us to recover (in a unified way) known results about uniformly bounded C0-semigroups and cosine functions as well as to prove new results for other families of operators. In particular, if A is the generator of an α-times integrated family of bounded and linear operators arising from the well-posedness of fractional differential equations of order β+1 then, we prove that the inequality |
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| Keywords: | Landau-Kolmogorov inequality Integrated semigroups Integrated cosine functions Abstract differential equations |
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