An extremal nonnegative sine polynomial
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
27/05/2014
27/05/2014
01/09/2003
|
Resumo |
For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed in such a way that {Kn(θ)} is a summability kernel. Thus, for each Pi 1 ≤ P ≤ ∞ and for any 27π-periodic function f ∈ Lp [-π, π], the sequence of convolutions Kn * f is proved to converge to f in Lp[-ππ]. The pointwise and almost everywhere convergences are also consequences of our construction. |
Formato |
759-774 |
Identificador |
http://dx.doi.org/10.1216/rmjm/1181069926 Rocky Mountain Journal of Mathematics, v. 33, n. 3, p. 759-774, 2003. 0035-7596 http://hdl.handle.net/11449/67393 10.1216/rmjm/1181069926 WOS:000220011400001 2-s2.0-1642296780 2-s2.0-1642296780.pdf |
Idioma(s) |
eng |
Relação |
Rocky Mountain Journal of Mathematics |
Direitos |
openAccess |
Palavras-Chave | #Convergence #Extremal polynomial ultraspherical polynomials #Nonnegative sine polynomial #Positive summability kernel |
Tipo |
info:eu-repo/semantics/article |