Publication
A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems.
| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 244.32 KB | Adobe PDF |
Advisor(s)
Abstract(s)
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.
Description
Copyright © 2005 Elsevier Inc. All rights reserved.
Keywords
Riemann-Hilbert Problem Bounded Canonical Factorization Almost-Periodic Function Corona Problem Finite-Interval Convolution Operator
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.
Publisher
Elsevier