Related papers: $R$-analytic functions

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…

Let $K$ be a finite extension of $\mathbb{Q}_p$ that is totally ramified over $\mathbb{Q}_p$. The set $\mathcal{M}\mathcal{F}(K)$ consists of power series in $1+zK[[z]]$ that are solutions of differential operators in $K(z)[d/dz]$ equipped…

Minimal representations of a real reductive group G are the `smallest' irreducible unitary representations of G. We discuss special functions that arise in the analysis of L^2-model of minimal representations.

Let $(K,\nu)$ be an arbitrary-rank valued field, $R_\nu$ its valuation ring, $K(\alpha)/K$ a separable finite field extension generated over $K$ by a root of a monic irreducible polynomial $f\in R_\nu[X]$. We give necessary and sufficient…

If $R$ is a real analytic set in $\C^n$ (viewed as $\R^{2n}$), then for any point $p\in R$ there is a uniquely defined germ $X_p$ of the smallest complex analytic variety which contains $R_p$, the germ of $R$ at $p$. It is shown that if $R$…

For a split reductive group $G$ over a finite extension $L$ of ${\mathbb Q}_p$, and a parabolic subgroup $P \subset G$ we introduce a category ${\mathcal O}^P$ which is equipped with a forgetful functor to the parabolic category ${\mathcal…

We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit…

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to…

The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format $\mathcal{F}$, recording information like the number of variables and…

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also…

This paper answers several open questions around structures with o-minimal open core. We construct an expansion of an o-minimal structure $\mathcal{R}$ by a unary predicate such that its open core is a proper o-minimal expansion of…

We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation…

Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid…

The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…

The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point…

In the first half of twentieth century the theory of complex analytic functions and of their zerosets was fully developed. The definition of holomorphic function has a local nature. Germs of holomorphic functions form a distinguished…

Let $k$ be a perfect complete valued field with a nontrivial non-archimedean norm $|\cdot|$ and $\omega\in k$ with $0<|\omega|<1.$ Let $X$ be a reduced and normal $k$-analytic space. Then $O^{\circ}\simeq…

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into $L^\infty(\mathbb R^n)$ is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to…