TY - JOUR

T1 - Constructive almost periodic factorization of some triangular matrix functions

AU - Câmara, M. C.

AU - Karlovich, Yu I.

AU - Spitkovsky, I. M.

N1 - Funding Information:
✩ A substantial portion of this work was conducted during the visits of Karlovich and Spitkovsky to Instituto Superior Técnico, supported by the FCT Project PTDC/MAT/81385/2006 (Portugal). The authors were also partially supported by FCT through the Program POCI 2010/FEDER (Portugal), the SEP-CONACYT Project No. 25564 (Mexico), and by the William & Mary sabbatical research leave funding, respectively. * Corresponding author. E-mail addresses: cristina.camara@math.ist.utl.pt (M.C. Câmara), karlovich@uaem.mx (Yu.I. Karlovich), ilya@math.wm.edu, imspitkovsky@gmail.com (I.M. Spitkovsky).

PY - 2010/7/15

Y1 - 2010/7/15

N2 - A factorability criterion is obtained constructively, and the respective factorization obtained explicitly, for 2 × 2 triangular almost periodic matrix functions of the form [(eλ, 0; f, e- λ)]. Here f = c- 1 e- α - c0 + c1 eβ, eμ (x) : = ei μ x, cj are non-zero constants and 0 < α, β, α + β < λ ≤ α + β + max {α, β} with α / β being irrational. Note that the factorization problem, even for triangular matrix functions as above with an arbitrary trinomial f, is open. The result obtained is yet another step towards its solution.

AB - A factorability criterion is obtained constructively, and the respective factorization obtained explicitly, for 2 × 2 triangular almost periodic matrix functions of the form [(eλ, 0; f, e- λ)]. Here f = c- 1 e- α - c0 + c1 eβ, eμ (x) : = ei μ x, cj are non-zero constants and 0 < α, β, α + β < λ ≤ α + β + max {α, β} with α / β being irrational. Note that the factorization problem, even for triangular matrix functions as above with an arbitrary trinomial f, is open. The result obtained is yet another step towards its solution.

KW - Almost periodic factorization

UR - http://www.scopus.com/inward/record.url?scp=77949773446&partnerID=8YFLogxK

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U2 - 10.1016/j.jmaa.2010.01.052

DO - 10.1016/j.jmaa.2010.01.052

M3 - Article

AN - SCOPUS:77949773446

VL - 367

SP - 416

EP - 433

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -