P-adic counterpart of Mikusinski's operational calculus and its applications to the Fourier and the Mahler expansions of locally constant functions
The p-adic counterpart of Mikusinski's operational calculus based on C(Z ; Q ) and the discrete Laplace convolution are considered. Some elements of Mikusinski's field are presented. A notion of a p-adic exponent is generalized. Applications to the Fourier and the Mahler expansions of locally constant functions and the convolution of two ball indicators are demonstrated Two ways of applying the calculus lead to the Fourier expansion for the fractional part of a p-adic number.