The aim of this paper is to give the asymptotic expansion of the coe cients in the Chebyshev series expansion of a function possessing algebraic or logarithmic interior singularities. Some numerical examples are given.
Asymptotic similarities of Fourier and Riemann coefficients
β Scribed by Chin-Hung Ching; Charles K Chui
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 221 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L 1 or the real Hardy spaces defined on IR n , where n β₯ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H 1 (IR) into L 1 (IR) and from L 1 (IR) into weak -L 1 (IR). We
We shall show that the oscillations observed by R. S. Strichartz in the Fourier transforms of self-similar measures have a large-scale renormalisation given by a Riesz measure. Vice versa the Riesz measure itself will be shown to be self-similar around every triadic point.
Fourier Jacobi series with nonnegative Fourier Jacobi coefficients are considered. Under special restrictions on the Jacobi weight function, we establish in terms of Fourier Jacobi coefficients a necessary and sufficient condition in order that the sum of the Fourier Jacobi series should possess cer