Abstract
At present there are only a few approximate identity kernels for the Walsh system, for example, the p N -truncated Dirichlet kernel D p N − 1 ( t) = ∑ j = 0 p N − 1 w j ( t) [6]; the Abel-Poisson kernel λ γ ( t) = ∑ k = 0 ∞ γ k w k ( t) [3], and so on. In [6], Zheng has introduced a new kind of approximate identity kernels for the Walsh system—the kernels of product type. In the present paper we discuss the approximation properties of such product type kernels. Estimates of their moments as well as a direct approximation theorem are obtained. Then, to establish an inverse approximation theorem, we need the p-adic derivative of product type kernels and we estimate this derivative in L 1-norm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.