Generalized Ces `aro operators, fractional finite differences and Gamma\n functions

2017/04/22 by Luciano Abadia, Abadia, Luciano, Pedro J. Miana +1 · 1 citation
Mathematics · #33B15 #40G05 #47A10 #47B38 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1704.06859

openalex publication_date 2017/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a complete spectral research of generalized\nCes `aro operators on Sobolev-Lebesgue sequence spaces. The main idea is to\nsubordinate such operators to suitable C<sub>0</sub>-semigroups on these sequence\nspaces. We introduce that family of sequence spaces using the fractional finite\ndifferences and we prove some structural properties similar to classical\nLebesgue sequence spaces. In order to show the main results about fractional\nfinite differences, we state equalities involving sums of quotients of Euler's\nGamma functions. Finally, we display some graphical representations of the\nspectra of generalized Ces `aro operators.\n

Cited by

• Norm of the Cesàro operator between some spaces of analytic functions

Related

• On the boundedness of generalized Cesàro operators on Sobolev spaces
• Spectral properties of generalized Cesàro operators in sequence spaces
• Cesaro operators on the Hardy spaces of the half-plane
• Functions of continuous Cesáro operators
• The Cesàro operator on power series spaces