Constructive almost periodic factorization of some triangular matrix functions |
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Authors: | MC Câmara |
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Institution: | a Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal b Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, C.P. 62209 Cuernavaca, Morelos, Mexico c Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA |
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Abstract: | A factorability criterion is obtained constructively, and the respective factorization obtained explicitly, for 2×2 triangular almost periodic matrix functions of the form . Here f=c−1e−α−c0+c1eβ, eμ(x):=eiμx, 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. |
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Keywords: | Almost periodic factorization |
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