Ingham-Type Inequalities and Riesz Bases of Divided Differences

• Autorzy: Avdonin S. , Moran W.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

simultaneous controllability; string equation; beam equation; Riesz bases; divided differences

PL

bazy Riesza; sterowanie jednoczesne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: Vol. 11, no 4
• Strony: 803--820
• Opis fizyczny: Bibliogr. 37 poz.

Twórcy

autor

Avdonin S.

autor

Moran W.

• Department of Mathematical Sciences University of Alaska Fairbanks P.O. Box 756660, Fairbanks, AK 99775-6660, U.S.A.,