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Construction of sampling and interpolating sequences for multi-band signals. The two-band case

Avdonin S., Bulanova A., Moran W.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 2

143-156

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.

Controllability types of a circular membrane with rotationally symmetric data

Avdonin S., Ivanov S.

Control and Cybernetics

1999

Vol. 28, no 3

383-396

Various controllability types are demonstrated for a circular membrane with rotationally symmetric initial data and boundary control depending on time only. We prove that the set of initial states, which can be steered to rest in the critical time interval (equal to the diameter of the membrane) by means of [L^2]-controls is dense in the energy space but contains no eigenmode. We also show that any initial data from a Sobolev space can be transferred to a stationary state. The proof is based on study of exponential families arising in the approach using the method of moments.