TY - JOUR

T1 - Constructive factorization of some almost periodic triangular matrix functions with a quadrinomial off diagonal entry

AU - Bastos, M. A.

AU - Bravo, A.

AU - Karlovich, Yu I.

AU - Spitkovsky, I. M.

N1 - Funding Information:
✩ This work was sponsored by FACC/FCT (Portugal), in particular during the visits of Yuri Karlovich and Ilya Spitkovsky at IST in the first half of 2009, when this project was started. Yuri Karlovich was also partially supported by the SEP-CONACYT Project No. 25564 (México), and Ilya Spitkovsky by the William & Mary sabbatical research leave funding. * Corresponding author. E-mail addresses: abastos@math.ist.utl.pt (M.A. Bastos), abravo@math.ist.utl.pt (A. Bravo), karlovich@uaem.mx (Yu.I. Karlovich), ilya@math.wm.edu, imspitkovsky@gmail.com (I.M. Spitkovsky).

PY - 2011/4/15

Y1 - 2011/4/15

N2 - Using an abbreviation e? to denote the function ei?x on the real line R, let G=[e?0fe??], where f is a linear combination of the functions e?, e?, e???, e??? with some (0<)?,?<?. The criterion for G to admit a canonical factorization was established recently by Avdonin, Bulanova and Moran (2007) [1]. We give an alternative approach to the matter, proving the existence (when it does take place) via deriving explicit factorization formulas. The non-existence of the canonical factorization in the remaining cases then follows from the continuity property of the geometric mean.

AB - Using an abbreviation e? to denote the function ei?x on the real line R, let G=[e?0fe??], where f is a linear combination of the functions e?, e?, e???, e??? with some (0<)?,?<?. The criterion for G to admit a canonical factorization was established recently by Avdonin, Bulanova and Moran (2007) [1]. We give an alternative approach to the matter, proving the existence (when it does take place) via deriving explicit factorization formulas. The non-existence of the canonical factorization in the remaining cases then follows from the continuity property of the geometric mean.

KW - Almost periodic factorization

UR - http://www.scopus.com/inward/record.url?scp=78650707290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650707290&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2010.11.037

DO - 10.1016/j.jmaa.2010.11.037

M3 - Article

AN - SCOPUS:78650707290

VL - 376

SP - 625

EP - 640

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -