Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2005-16

December 2005

On the coherence of some irrational transfer function classes

Amol Sasane


Let D, T denote the unit disc and unit circle with center 0, respectively, in the complex plane C. If S is a subset of T, then let A_S denote the set of complex-valued functions defined on D U S, that are analytic in D, and continuous and bounded on D U S. Then A_S is a ring with pointwise addition and multiplication. We prove that if the intersection of S with the set of limit points of S is not empty, then the ring A_S is not coherent.

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Last modified: 6th December 2005