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Full-Text Articles in Other Mathematics
Matrix-J-Unitary Non-Commutative Rational Formal Power Series, Daniel Alpay, D. S. Kalyuzhnyi-Verbovetzkii
Matrix-J-Unitary Non-Commutative Rational Formal Power Series, Daniel Alpay, D. S. Kalyuzhnyi-Verbovetzkii
Mathematics, Physics, and Computer Science Faculty Articles and Research
Formal power series in N non-commuting indeterminates can be considered as a counterpart of functions of one variable holomorphic at 0, and some of their properties are described in terms of coefficients. However, really fruitful analysis begins when one considers for them evaluations on N-tuples of n × n matrices (with n = 1, 2, . . .) or operators on an infinite-dimensional separable Hilbert space. Moreover, such evaluations appear in control, optimization and stabilization problems of modern system engineering.
In this paper, a theory of realization and minimal factorization of rational matrix-valued functions which are J-unitary on the imaginary …