Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2007-08

March 2007

A Spectrally Minimal Realization Formula for H^∞(D)

Kalle Mikkola and Amol Sasane

In this article we prove a representation theorem for H^∞(D) functions, such that the realization formula is spectrally minimal in the following sense: the spectrum of the main operator in the realization intersects the unit circle precisely at those points where the given function has no holomorphic extension. We also extend this result to operator-valued H^∞ functions.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk