On the norms and minimal properties of de la Vallee Poussin's type operators Academic Article

abstract

• 2018, Springer-Verlag GmbH Austria, part of Springer Nature. In this paper we consider the de la Valle Poussins type operators Hrn,snHrn,sn:=Frn+Frn+1+..+Fsn-1(s-r)n,where Fk are classical Fourier projections onto k (the space of trigonometric polynomials of degree less than or equal to k). We determine when Hn,sn is the minimal generalized projection and provide the asymptotic behavior of the norm Hn,sn. Additionally, we contrast the results obtained for the trigonometric system to the results obtained for the Rademacher system.

authors

• Foucart, Simon

published proceedings

• MONATSHEFTE FUR MATHEMATIK

author list (cited authors)

• Deregowska, B., Foucart, S., Lewandowska, B., & Skrzypek, L.

citation count

• 0

publication date

• April 2018

publisher

• Springer Nature  Publisher

keywords

• De La Vallee Poussin's Operators
• Generalized Projections
• Minimal Projections

Digital Object Identifier (DOI)

• 10.1007/s00605-018-1159-x

start page

• 601

end page

• 619

volume

• 185

issue

• 4

URL

• http://dx.doi.org/10.1007/s00605-018-1159-x