Abstract
We consider the p-adic counterpart of Mikusinski’s operational calculus based on the algebra C(ℤp) of continuous functions on ℤp taking values in ℂp and equipped with the discrete Laplace convolution. Elements of the field (hyperfunctions) corresponding to shift operators, difference operators, and the indefinite sum operator are considered. A notion of p-adic exponent is generalized. Applications to the Fourier and the Mahler expansions of the indicator function of a ball and the convolution of two indicator functions are provided. Two ways of applying the p-adic analog of Mikusinski’s operational calculus lead us to the Fourier expansion for the fractional part of a p-adic number.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: P-Adic Numbers, Ultrametric Analysis, and Applications
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.
