Functions of continuous Cesáro operators

2024/11/23 by Mirotin, Adolf
#47B15 #47B38 (Secondary) #47G10 (Primary) 45P05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2411.15578

Abstract

We describe holomorphic functions and fractional powers of Cesáro operators in L²(ℝ), L²(ℝ₊), and L²[0,1]. Logarithms of Cesáro operators are introduced as well and their spectral properties are studied. Several examples are considered.

Related

• The Cesaro operator
• Cesàro operators on the space of analytic functions with logarithmic growth
• Cesaro operators on the Hardy spaces of the half-plane
• Mean ergodic properties of the continuous Cesàro operators
• Generalized Ces `aro operators, fractional finite differences and Gamma\n functions