Some stability theorems for nonharmonic Fourier series

Some Stability Theorems for Nonharmonic Fourier Series

The theory of nonharmonic Fourier series in L2(-ir,tr) is concerned with the completeness and expansion properties of sets of complex exponentials {e'x"'}. It is well known, for example, that the completeness of the set {e'x"'} ensures that of {e'^"'} whenever 2 lA„ ~~ M»l < oo. In this note we establish two results which guarantees that if {elX"'} is a Schauder basis for l}(—n, it), then [e'^"...

Pointwise and directional regularity of nonharmonic Fourier series

We investigate how the regularity of nonharmonic Fourier series is related to the spacing of their frequencies. This is obtained by using a transform which simultaneously captures the advantages of the Gabor and Wavelet transforms. Applications to the everywhere irregularity of solutions of some PDEs are given. We extend these results to the anisotropic setting in order to derive directional ir...

Some Stability Theorems for Polygons of Polynomials

-, “Generalized Riccati equations for two-point boundaly value descriptor systems,” in Proc. 26th IEEE Conf: Decision Contr., Los Angeles, CA, 1987. H. E. Rauch, F. Tung, and C. T. Striebel, “Maximum likelihood estimates of linear systems,” J. AZAA, vol. 3, pp. 1445-1450, 1965. L. R. Riddle and H. L. Weinert, “Fast algorithms for the reconstruction of images from hyperbolic systems,” in Proc. 2...

Stability theorems for some functional differential equations

Stability Theorems for Fourier Frames and Wavelet Riesz Bases

In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis our estimate reduces to Kadec’ optimal 1/4 re...