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Zbl 1200.42026
Ren, Guangbin; Chen, Qiuhui; Cerejeiras, Paula; Kähler, Uwe
Chirp transforms and chirp series.
(English)
[J] J. Math. Anal. Appl. 373, No. 2, 356-369 (2011). ISSN 0022-247X

The theory of non harmonic Fourier series was originated by Paley and Wiener, and more recently, in a series of papers, many questions were studied. The authors introduce an integral version of the non-harmonic Fourier series, called Chirp transform. It becomes from the Fourier integral transform, if one replaces the kernel by $e^{i\phi(t)\theta(\omega)}$, for certain functions $\phi$ and $\theta$, which is called Chirp atom. They consider the Chirp series, which is a discrete version of the Chirp transform associated to the Chirp atoms. They also establish the Chirp version of the Shannon sampling theorem and the Poisson summation formula. Finally they show that Chirp transform can be applied to some certain differential equations with non-constant coefficients.
[Chrysoula G. Kokologiannaki (Patras)]
MSC 2000:
*42C20 Rearrangements and other transformations of orthogonal series
42A38 Fourier type transforms, one variable

Keywords: chirp transform; chirp series; Hermite polynomials; Poisson summation formula

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