Factorizations, Riemann-Hilbert problems and the corona theorem

M. C. Câmara, C. Diogo, Yu I. Karlovich, Ilya Spitkovsky

Research output: Contribution to journalArticle

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, when the factorization multiples belong to the algebra generated by the functions eλ(x) := eiλx, λ ε R. Connections with the corona problem are discussed. Based on those, constructive factorization criteria are derived for several types of triangular 2 × 2 matrices with diagonal entries e±λ and non-zero off diagonal entry of the form a?e?β + a+e? with ?, β ≥? +β >nd a± analytic and bounded in the upper/lower half plane.

Original languageEnglish (US)
Pages (from-to)852-878
Number of pages27
JournalJournal of the London Mathematical Society
Volume86
Issue number3
DOIs
StatePublished - Jan 1 2012

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Corona Theorem
Riemann-Hilbert Problem
Factorization
Corona
Almost Periodic
Half-plane
Real Line
Hilbert
Solvability
Triangular
Boundary Value Problem
Cover
Algebra
Coefficient

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Factorizations, Riemann-Hilbert problems and the corona theorem. / Câmara, M. C.; Diogo, C.; Karlovich, Yu I.; Spitkovsky, Ilya.

In: Journal of the London Mathematical Society, Vol. 86, No. 3, 01.01.2012, p. 852-878.

Research output: Contribution to journalArticle

Câmara, M. C. ; Diogo, C. ; Karlovich, Yu I. ; Spitkovsky, Ilya. / Factorizations, Riemann-Hilbert problems and the corona theorem. In: Journal of the London Mathematical Society. 2012 ; Vol. 86, No. 3. pp. 852-878.
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