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1
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Ingham-type inequalities and Riesz bases of divided differences

100%
Avdonin S., Moran W.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 4
803-820
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.
2
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Construction of sampling and interpolating sequences for multi-band signals. the two-band case

81%
Avdonin S., Bulanova A., Moran W.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 2
143-156
EN
Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
3
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Nilpotent groups with $T_{1}$ primitive ideal spaces

60%
Carey A. L., Moran W.
Studia Mathematica
|
1986
|
tom 83
|
nr 1
25-32
4
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In general, Bernoulli convolutions have independent powers

51%
Brown G., Moran W.
Studia Mathematica
|
1973
|
tom 47
|
nr 2
141-152
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