The degree of ill-posedness for some composition governed by the Cesaro operator

2024/01/21 by Yu Deng, Deng, Yu, Hans-Jürgen Fischer +3
Mathematics · #40G05 (Secondary) #47A52 (Primary) #47B06 #65J20 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.11411

openalex publication_date 2024/01/21 · openalex created_date 2024/01/24 · openalex updated_date 2026/07/28

Abstract

In this article, we consider the singular value asymptotics of compositions of compact linear operators mapping in the real Hilbert space of quadratically integrable functions over the unit interval. Specifically, the composition is given by the compact simple integration operator followed by the non-compact Ces`aro operator possessing a non-closed range. We show that the degree of ill-posedness of that composition is two, which means that the Ces`aro operator increases the degree of illposedness by the amount of one compared to the simple integration operator.

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