Almost Periodic Factorization of Some Triangular Matrix Functions
M. Cristina Câmara, Yuri I. Karlovich, Ilya M. Spitkovsky · Birkhäuser Basel eBooks · 2009
The paper is devoted to matrices of the form $$ G(x) = \left[ {\begin{array}{*{20}c} {e^{i\lambda x} } & 0 \\ {f(x)} & {e^{ - i\lambda x} } \\ \end{array} } \right], $$ , with almost periodic off-diagonal entry f. Some new cases are found, in terms of the Bohr-Fourier spectrum of f, in which G is factorable. Formulas for the partial indices are derived and, under additional constraints, the factorization itself is constructed explicitly. Some a priori conditions on the Bohr-Fourier spectra of the factorization factors (provided that a canonical factorization exists) are also given.