In this talk, we present a complete spectral research of generalized Cesàro operators on Sobolev-Lebesgue sequence spaces. The main idea is to subordinate such operators to suitable \(C_0\) -semigroups on these sequence spaces. We introduce that family of sequence spaces using the fractional finite differences and we prove some structural properties similar to classical Lebesgue sequence spaces. In order to show the main results about fractional finite differences, we state equalities involving sums of quotients of Euler’s Gamma functions. Finally, we display some graphical representations of the spectra of generalized Cesàro operators. Main results of this talk are included in a joint paper with L. Abadias ([1]).
References
[1] L. Abadias and P.J. Miana. Generalized Cesàro operators, fractional finite differences and Gamma functions. J. Funct. Anal., 274 , (2018), 1424–1465.
Partially supported by Project MTM2016-77710-P, DGI-FEDER, of the MCYTS and Project E-64, D.G. Aragón, Universidad de Zaragoza, Spain.