In this paper the partial exact controllability of an elastic spherical membrane is proved. The reachability problem for the integrodifferential equation, introduced for the vibrations of the meridional displacement, is solved. The main result is a generalization of a Ingham’s theorem on nonharmonic Fourier series.

In this paper, we study the exact boundary controllability of linear fourth-order Schrödinger equation, with variable physical parameters and clamped conditions on a bounded interval. The control acts first spatial derivative at right endpoint. We prove that system is exactly controllable any time $$T>0$$ . proofs are based detailed spectral analysis use nonharmonic Fourier series.

for all f ∈ H.A and B are called frame bounds.The sequence is called a tight frame if A = B. The sequence is called Bessel if the second inequality above holds. In this case, B is called the Bessel bound. Frames were first introduced by Duffin and Schaeffer [1] in the context of nonharmonic Fourier series, and today they have applications in a wide range of areas. A frame can be considered as a...

We study the action of A on f ∈ L 2 (R) and on its wavelet coefficients, where A = (a lmjk) lmjk is a double infinite matrix. We find the frame condition for A-transform of f ∈ L 2 (R) whose wavelet series expansion is known. 1. Introduction. The notation of frame goes back to Duffin and Schaeffer [7] in the early 1950s to deal with the problems in nonharmonic Fourier series. There has been ren...

Spectral reprojection techniques make possible the recovery of exponential accuracy from the partial Fourier sum of a piecewise-analytic function, essentially conquering the Gibbs phenomenon for this class of functions. This paper extends this result to non-harmonic partial sums, proving that spectral reprojection can reduce the Gibbs phenomenon in nonharmonic reconstruction as well as remove r...

We give precise conditions under which the real interpolation space [Y0, X1]θ,p coincides with a closed subspace of [X0, X1]θ,p when Y0 is a closed subspace of codimension one. We then apply this result to nonharmonic Fourier series in Sobolev spaces Hs(−π, π) when 0 < s < 1. The main result: let E be a family of exponentials exp(iλnt) and E forms an unconditional basis in L2(−π, π). Then there...

in this paper, we propose a new residual analysis method using fourier series transform into fuzzy time series model for improving the forecasting performance. this hybrid model takes advantage of the high predictable power of fuzzy time series model and fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...

Precise conditions are given under which the real interpolation space [Y0, X1]θ,p coincides with a closed subspace of [X0,X1]θ,p when Y0 is a closed subspace of codimension one. This result is applied to the study of nonharmonic Fourier series in the Sobolev spaces Hs(−π, π) with 0 < s < 1. The main result looks like this: if {eiλnt} is an unconditional basis in L2(−π, π), then there exist two ...

Abstract. In this paper we prove a discrete version of the classical Ingham inequality for nonharmonic Fourier series whose exponents satisfy a gap condition. Time integrals are replaced by discrete sums on a discrete mesh. We prove that, as the mesh becomes finer and finer, the limit of the discrete Ingham inequality is the classical continuous one. This analysis is partially motivated by cont...