Integer-valued polynomial in valued fields with an application to discrete dynamical systems

TL;DR: In this article, the authors prove a similar result for odd and even functions in a more general framework by considering the Banach space C (E, K ) of continuous functions, where K is any valued field and E is any symmetric regular compact subset of K.

TL;DR: In this paper, it was shown that the generating set of integer-valued polynomials obtained by de Shalit and Iceland by means of Lubin-Tate formal group laws is minimal.

TL;DR: The notion of pseudo-monotone sequence and pseudo-limit in the sense of Chabert was introduced in this article, which generalizes the classical notions of pseudoconvergent sequence and pseudoregressive limit by Ostrowski and Kaplansky, respectively.

TL;DR: In this paper, the additive structure of integer-valued polynomials has been studied in combinatorial, arithmetical, algebraic, ultrametric, or dynamical nature.

TL;DR: In this paper, the authors derived a simple expression ford(X, F) explicitly in terms of the coefficients of F, using a generalized notion of "factorial" introduced by the author in a previous paper.

TL;DR: In this article, the authors consider isometric dynamical systems on a Legendre set of a discrete valuation domain with finite residual field and characterise the minimality of the system by using the structure of the Legendre sequence of the set and also find the corresponding machine to which such a minimal system is conjugate.

TL;DR: In this article, the authors studied the properties of ultrametric matrices and proved explicit formulas in the case where D is a Dedekind domain with infinite residue fields, and then they extended these results to the case of number fields.

TL;DR: In this paper, the authors generalize notions and results obtained by Amice for regular compact subsets S of a local field K and extended by Bhargava to general compact sets of K. They show that these subsets still have strong properties such as having v-orderings, which satisfy a generalized Legendre formula.