Publication
A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems.
| dc.contributor.author | Câmara, Maria Cristina | |
| dc.contributor.author | Santos, António Ferreira dos | |
| dc.contributor.author | Martins, Maria do Carmo | |
| dc.date.accessioned | 2014-01-15T15:44:30Z | |
| dc.date.available | 2014-01-15T15:44:30Z | |
| dc.date.issued | 2006-01-18 | |
| dc.date.updated | 2013-12-27T17:22:37Z | |
| dc.description | Copyright © 2005 Elsevier Inc. All rights reserved. | en |
| dc.description.abstract | The factorization of almost-periodic triangular symbols, G, associated to finite-interval convolution operators is studied for two classes of operators whose Fourier symbols are almost periodic polynomials with spectrum in the group αZ+βZ+ZαZ+βZ+Z (α,β∈]0,1[α,β∈]0,1[, α+β>1α+β>1, α/β∉Qα/β∉Q). The factorization problem is solved by a method that is based on the calculation of one solution of the Riemann-Hilbert problem GΦ+=Φ−GΦ+=Φ− in L∞(R)L∞(R) and does not require solving the associated corona problems since a second linearly independent solution is obtained by means of an appropriate transformation on the space of solutions to the Riemann-Hilbert problem. Some unexpected, but interesting, results are obtained concerning the Fourier spectrum of the solutions of GΦ+=Φ−GΦ+=Φ−. In particular it is shown that a solution exists with Fourier spectrum in the additive group αZ+βZαZ+βZ whether this group contains ZZ or not. Possible application of the method to more general classes of symbols is considered in the last section of the paper. | en |
| dc.identifier.citation | Câmara, M.C.; Santos, A.F. dos; Martins, M.C. (2006). "A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems". Journal of functional Analysis, 235(2): 559-592. http://dx.doi.org/10.1016/j.jfa.2005.11.011. | en |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.uri | http://hdl.handle.net/10400.3/2603 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.publisher | Elsevier | por |
| dc.relation.publisherversion | http://dx.doi.org/10.1016/j.jfa.2005.11.011 | por |
| dc.subject | Riemann-Hilbert Problem | en |
| dc.subject | Bounded Canonical Factorization | en |
| dc.subject | Almost-Periodic Function | en |
| dc.subject | Corona Problem | en |
| dc.subject | Finite-Interval Convolution Operator | en |
| dc.title | A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems. | en |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 592 | por |
| oaire.citation.issue | (2) | por |
| oaire.citation.startPage | 559 | por |
| oaire.citation.title | Journal of functional Analysis | en |
| oaire.citation.volume | 235 | por |
| rcaap.rights | restrictedAccess | por |
| rcaap.type | article | por |