ISSN:
1420-8989
Keywords:
Primary 30E05
;
Secondary 30E10
;
42A70
;
42B30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This article gives necessary and sufficient conditions for local solutions to several very general constrained optimization problems over spaces of analytic functions. The results presented here have many applications, a particular instance of which is the sup-norm approximation of functions continuous on the unit circle in the complex plane by functions continuous on the circle and analytic on the open disk and whose Fourier coefficients satisfy prescribed linear relations. Also, the results in this article generalize Nevanlinna-Pick and Caratheodory-Fejer Interpolation results to allow values of arbitrary derivatives of functions to be assigned or merely bounded. Classically, NP and CF solve only problems with consecutive derivatives specified. In engineering, constraints on the Fourier coefficients of a frequency response function correspond to constraints on its “time domain” behavior. Indeed the central problems of control theory involve both time and frequency domain constraints. That is precisely what the results in this paper handle.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01203384
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