fejér kernel
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2018 ◽  
Vol Volume-2 (Issue-3) ◽  
pp. 2466-2471
Author(s):  
Rajendra Bapurao Vhatkar ◽  
Dr. Vishwajeet S. Goswami ◽  

2009 ◽  
Vol 1 (2) ◽  
pp. 281-284
Author(s):  
M. Galaz-Larios ◽  
R. Garcia-Olivo ◽  
J. López-Bonilla

We show that the Fejér kernel generates the fifth-kind Chebyshev polynomials.Keywords: Kernels in Fourier series; Chebyshev polynomials.© 2009 JSR Publications.ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i2.2282


2007 ◽  
Vol 142 (1) ◽  
pp. 149-152 ◽  
Author(s):  
COLIN C. GRAHAM

AbstractPM(E) denotes the set of pseudomeasures on $\mathbb{R}$ with support in the closed set E ⊆ $\mathbb{R}$. Then y ∈ $\mathbb{R}$ is not in E if and only if there is a neighbourhood W of y with $\lim_{N\to\infty} \int_{-N}^{N}(1-{|t|}/{N})e^{2\pi itw}\cal{F} S(t)\,dt=0$ uniformly for w ∈ W and S ∈ PM(E) with ‖S‖PM ≤ 1. This improves previous results by adding “uniformly” and its scope. The proof uses the fact that squashing the central spike of the Fejer kernel leads to A-norm convergence.


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