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 language | American English |
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Journal | Journal of Mathematical Analysis and Applications |
Volume | 208 |
DOIs | |
State | Published - Apr 15 1997 |
Keywords
- Local field
- Riesz type kernels
- Ring of integers
DC Disciplines
- Mathematics