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Matrix Riemann-Hilbert problems with jumps across Carleson contours
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0001-6191-7769
2018 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 186, no 1, p. 111-152Article in journal (Refereed) Published
Abstract [en]

We develop a theory of n x n-matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour Gamma is a finite union of simple closed Carleson curves in the Riemann sphere. In particular, unbounded contours with cusps, corners, and nontransversal intersections are allowed. We introduce a notion of L-p-Riemann-Hilbert problem and establish basic uniqueness results and Fredholm properties. We also investigate the implications of Fredholmness for the unique solvability and prove a theorem on contour deformation.

Place, publisher, year, edition, pages
SPRINGER WIEN , 2018. Vol. 186, no 1, p. 111-152
Keywords [en]
Matrix Riemann-Hilbert problem, Cauchy integral, Carleson contour
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-227214DOI: 10.1007/s00605-017-1019-0ISI: 000430395800007Scopus ID: 2-s2.0-85011002995OAI: oai:DiVA.org:kth-227214DiVA, id: diva2:1211791
Note

QC 20180531

Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approved

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Lenells, Jonatan

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