1. Iwasawa functions, p-adic measures, and distributions 1 1.1. Some preliminaries 1 1.2. Iwasawa functions and the Iwasawa algebra 3 1.3. Iwasawa functions and interpolation 4 1.4. p-adic distributions and p-adic measures 8 2. The p-adic L-functions of Dirichlet characters 10 2.1. Preliminaries 10 2.2. Iwasawa’s construction 12 3. The p-adic L-functions of modular forms 15 3.1. Preliminaries 1...

We show that translations and dilations of a p–adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p–adic wavelets. In this sense the continuous p–adic wavelet transform coincides with the discrete p–adic wavelet transform. The p–adic multiresolution approximation is introduced and relation with the real multiresolution approximat...

Using an adelic approach we simultaneously consider real and padic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL(2, Q), SL(2, Q) and SL(2, Z) groups. In particular, we investigate behavior of these adelic systems when fixed points are rational. It is shown that any of these rational fixed points is p-adic indifferent...

In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spa...