Volume no :4, Issue no: 1, January 2010

Journal of Mathematical Sciences: Advances and Applications

ON THE RIEMANN-LEBESGUE LEMMA WITH A NONHARMONIC KERNEL

Author's: Nassar H. S. Haidar
Pages: [9] - [26]
Received Date: May 2, 2009
Submitted by: Sunggeum Hong

Abstract

Proofs are provided to the Riemann-Lebesgue Lemma for general periodic and wavelet-like kernels and within the context of a recently advanced [6] nonharmonic form for this lemma, with a scale-frequency duplicated asymptotic parameter. We also introduce the concept of a symmetrized Riemann integral and demonstrate the existence of a Riemann-Lebesgue property for it.

Keywords

Riemann-Lebesgue Lemma, wavelet-like kernel, nonharmonic Fourier analysis.