Related papers: On Those Analytic Functions of One Variable which …
The hyperbolic Ax-Lindemann-Weierstrass conjecture is a functional algebraic independence statement for the uniformizing map of an arithmetic variety. In this paper we provide a proof of this conjecture, generalizing previous work of…
Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…
We prove that every arc-analytic semialgebraic function on an arc-symmetric set admits an arc-analytic semialgebraic extension to the whole ambient Euclidean space.
We give a new proof of a classical theorem on approximation of continuous functions on totally real sets
Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…
A function of two variables F(x,y)is universal iff for every other function G(x,y) there exists functions h(x) and k(y) with G(x,y) = F(h(x),k(y)) Sierpinski showed that assuming the continuum hypothesis there exists a Borel function F(x,y)…
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
In this paper has been proved the pluripolarity of graphs of algebroid functions
We adapt the notion of an algebraic theory to work in the setting of quasicategories developed recently by Joyal and Lurie. We develop the general theory at some length. We study one extended example in detail: the theory of commutative…
We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of…
The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions within these spaces, and in particular, we provide an…
It is shown (Theorem A and its corollary) that if g is any nonconstant nonunivalent analytic function on a half-plane H and if D is either a half-plane or a smoothly bounded Jordan domain, then there is a function f on D for which f'(D)…
Emphasizing the role of Gerstenhaber algebras and of higher derived brackets in the theory of Lie algebroids, we show that the several Lie algebroid brackets which have been introduced in the recent literature can all be defined in terms of…
We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…