Related papers: The Maillet--Malgrange type theorem for generalize…
A Maillet-Malgrange type theorem is proved for a Dulac series (in the general case, with complex exponents), which formally satisfies an analytical ordinary differential equation (ODE). This theorem allows to estimate the growth of the…
We propose a sufficient condition of the convergence of a generalized power series formally satisfying an algebraic (polynomial) ordinary differential equation. The proof is based on the majorant method.
A sufficient condition for the convergence of a generalized formal power series solution to an algebraic $q$-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power…
We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…
In this paper we prove a generalization of Montel's theorem for a class of first order elliptic equations with measurable coefficients involving Hodge-Dirac operators. We then apply this result to sequences of solutions of second order…
We propose an analytic proof of the Malgrange-Sibuya theorem concerning a sufficient condition of the convergence of a formal power series satisfying an ordinary differential equation. The proof is based on the majorant method and allows to…
For the generalized oscillator, we prove a Rellich type theorem, or characterize the order of growth of eigenfunctions. The proofs are given by an extensive use of commutator arguments invented recently by Ito and Skibsted. These arguments…
The question of the convergence of generalized formal power series (with complex power exponents) solutions of $q$-difference equations is studied in the situation where the small divisors phenomenon arises; a sufficient condition of…
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.
We propose a sufficient condition of the convergence of a power-log series that formally satisfies an algebraic ordinary differential equation (ODE) of arbitrary order. A general form and properties of the functional coefficients of such a…
We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…
A novel power series representation of the generalized Marcum $Q-$function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a…
The difference Galois theory of Mahler equations is an active research area. The present paper aims at developing the analytic aspects of this theory. We first attach a pair of connection matrices to any regular singular Mahler equation. We…
We derive a Liouville type result for special Lagrangian equations with certain "convexity" and restricted linear growth assumptions on the solutions.
We establish a version of the Beurling-Pollard theorem for operator synthesis and apply it to derive some results on linear operator equations and to prove a Beurling-Pollard type theorem for Varopoulos tensor algebras. Additionally we…
In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…
Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the approaches to study them is, firstly, to find formal solutions…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
Taylor's and Laurent's expansions of $G$-monogenic mappings taking values in the algebra of complex quaternion are obtained and singularities of these mappings are classified.