Ingham-type inequalities and Riesz bases of divided differences

• Autorzy: Sergei Avdonin , William Moran
• Języki publikacji: EN

Abstrakty

EN

We study linear combinations of exponentials e^{iλ_nt} , λ_n ∈ Λ in the case where the distance between some points λ_n tends to zero. We suppose that the sequence Λ 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 Λ is less than T/(2π), the family of divided differences can be extended to a Riesz basis in L^2 (0,T) by adjoining to {e^{iλ_nt}} a suitable collection of exponentials. Likewise, if the lower uniform density is greater than T/(2π), the family of divided differences can be made into a Riesz basis by removing from {e^{iλ_nt}} a suitable collection of functions e^{iλ_nt}. Applications of these results to problems of simultaneous control of elastic strings and beams are given.

Słowa kluczowe

EN

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

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 4
• Strony: 803-820

Daty

wydano

2001

otrzymano

2001-06-01

poprawiono

2001-09-01

Twórcy

autor

Sergei Avdonin

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

autor

William Moran

• Department of Mathematics and Statistics, Flinders University of South Australia, GPO Box 2100, Adelaide 5001, Australia

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