Abstract
Explicit factorization formulas are established for triangular almost periodic matrix functions with trinomial off diagonal terms in the so-called borderline cases. An application to a more general configuration via the Portuguese transformation also is given.
The work was partially supported by the SEP-CONACYT Project 25564 (Yuri Karlovich) and NSF grant DMS-0456625 (Ilya Spitkovsky).
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References
M.A. Bastos, Yu.I. Karlovich, I.M. Spitkovsky, and P.M. Tishin, On a new algorithm for almost periodic factorization, Recent progress in operator theory (Regensburg, 1995) (I. Gohberg, R. Mennicken, and C. Tretter, eds.), Operator Theory: Advances and Applications, vol. 103, Birkhäuser Verlag, Basel and Boston, 1998, pp. 53–74.
A. Böttcher, Yu.I. Karlovich, and I.M. Spitkovsky, Convolution operators and factorization of almost periodic matrix functions, Operator Theory: Advances and Applications, vol. 131, Birkhäuser Verlag, Basel and Boston, 2002.
M.C. Câmara, A.F. dos Santos, and M.C. Martins, A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems, J. Funct. Anal. 235 (2006), no. 2, 559–592.
M.C. Câmara, Yu.I. Karlovich, and I.M. Spitkovsky, Almost periodic factorization of some triangular matrix functions, Operator Theory: Advances and Applications, vol. 190, Birkhâuser Verlag, Basel and Boston, 2009, pp. 171–190.
I.P. Cornfeld, S.V. Fomin, and Ya.G. Sinaî, Ergodic theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 245, Springer-Verlag, New York, 1982, Translated from the Russian by A. B. Sosinskiî.
Yu.I. Karlovich and I.M. Spitkovsky, Factorization of almost periodic matrix functions, J. Math. Anal. Appl. 193 (1995), 209–232.
Yu.I. Karlovich, I.M. Spitkovsky, and R.A. Walker, Almost periodic factorization of block triangular matrix functions revisited, Linear Algebra Appl. 293 (1999), 199–232.
D. Quint, L. Rodman, and I.M. Spitkovsky, New cases of almost periodic factorization of triangular matrix functions, Michigan Math. J. 45 (1998), 73–102.
A. Rastogi, L. Rodman, and I.M. Spitkovsky, Almost periodic factorization of 2 × 2 matrix functions: New cases of off diagonal spectrum, Operator Theory: Advances and Applications 202, Birkhäuser Verlag, Basel and Boston, 2010, pp. 469–487 (this volume).
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Communicated by L. Rodman.
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Karlovich, Y.I., Spitkovsky, I.M. (2010). Almost Periodic Polynomial Factorization of Some Triangular Matrix Functions. In: Topics in Operator Theory. Operator Theory: Advances and Applications, vol 202. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0158-0_19
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DOI: https://doi.org/10.1007/978-3-0346-0158-0_19
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