Spectral Properties of the Reflection Operator in Two Dimensions

Document Type

Journal Article

Role

Author

Standard Number

0271-4132

Journal Title

Contemporary Mathematics

Volume

581

First Page

199

Last Page

215

Publication Date

2012

Abstract

We study spectral properties of the reflection operator (a singular integral operator arising naturally in connection with the radiosity equation which models the energy transfer between different parts of a surface by radiation) acting on L p spaces, p ∈ (1, ∞), on infinite angles in two dimensions. More specifically we establish an explicit characterization of the spectrum and spectral radius estimates for the reflection operator acting on L p spaces on an infinite angle in two dimensions. This type of analysis is relevant to the solvability of the radiosity equation with L p data since when the spectral radius is < 1, the solution can be explicitly expressed as a convergent Neumann series.

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