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Abstrakty
We study linear combinations of exponentials e^{i lambda_n t}, lambda_n in Lambda in the case where the distance between some points lambda_n tends to zero. We suppose that the sequence Lambda is a finite union of uniformly discrete sequences. In (Avdonin and Ivanov, 2001), necessary and sufficient conditions were given for the family of divided differences of exponentials to form a Riesz basis in space L^2 (0,T). Here we prove that if the upper uniform density of Lambda is less than T/(2 pi), the family of divided differences can be extended to a Riesz basis in L^2 (0,T) by adjoining to {e^{i lambda_n t} } a suitable collection of exponentials. Likewise, if the lower uniform density is greater than T/(2 pi), the family of divided differences can be made into a Riesz basis by removing from {e^{i lambda_n t} } a suitable collection of functions e^{i lambda_n t}. Applications of these results to problems of simultaneous control of elastic strings and beams are given.
Rocznik
Tom
Strony
803--820
Opis fizyczny
Bibliogr. 37 poz.
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autor
autor
- Department of Mathematical Sciences University of Alaska Fairbanks P.O. Box 756660, Fairbanks, AK 99775-6660, U.S.A., ffsaa@uaf.edu
Bibliografia
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0012-0037