Riesz Type Kernels Over the Ring of Integers of a Local Field

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Abstract

Let O denote the ring of integers of a local field. In this note we prove an approximation theorem for the Riesz type kernels {γμ, λ, }n∞ over O . The proof requires a sharp estimate of the Dirichlet kernel Dn ( x ) on P −1\ O , which may also have independent interest. As a consequence we solve the local field analog of 1 concerning rates of convergence of the Fejér sum on the Walsh system. Our approach has potential applications to other operators such as Cesáro means and Abel–Poisson means of “type I.”
Original languageAmerican English
JournalJournal of Mathematical Analysis and Applications
Volume208
DOIs
StatePublished - Apr 15 1997

Keywords

  • Local field
  • Riesz type kernels
  • Ring of integers

DC Disciplines

  • Mathematics

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