Factorization, Riemann-Hilbert problems and the corona problem

2011/03/10 by M. C. Camara, C. Diogo, Camara, M. C. +5
Mathematics · #42A75 #47A68 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:42A75 #msc:47A68 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1103.1935

32 pages

arxiv created 2011/03/10 · arxiv updated 2011/03/11

Abstract

The solvability of the Riemann-Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener-Hopf type factorization with bounded outer factors but rather general diagonal elements of its middle factor. This covers, in particular, the almost periodic setting. Connections with the corona problem are discussed. Based on those, constructive factorization criteria are derived for several types of triangular 2-by-2 matrices.

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