An inequality associated with some entire functions.
An Inequality for Trigonometric Polynomials
The main result says in particular that if is a trigonometric polynomial of degree n having all its zeros in the open upper half-plane such that |t(ξ)| ≥ μ on the real axis and cₙ ≠ 0, then |t’(ξ)| ≥ μn for all real ξ.
An inequality involving the absolute value of an entire function and the counting function of its zeros.
Analytic continuation of Dirichlet series.
The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series Σ0∞ an ζn2 (where 0 < |a| < 1) is nowhere continuable across {|ζ| = 1}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial differential equations...
Analytic First Integrals of Ordinary Differential Equations
Analytic functions in the unit disc sharing values in a sector
We deal with the uniqueness of analytic functions in the unit disc sharing four distinct values and obtain two theorems improving a previous result given by Mao and Liu (2009).
Analytic mappings between two ultrahyperelliptic surfaces.
Analytic mappings between two ultrahyperelliptic surfaces. (Short Communication).
Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1
For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where , satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ...
Analytic solutions of Böttcher's functional equation in the unit disk.
Angular Limits of Holomorphic Functions Which Satisfy an Integrability Condition.
Annular functions form a residual set.
Applications de la théorie de Nevanlinna p-adique.
Applications of the -adic Nevanlinna theory to functional equations
Let be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. We apply the -adic Nevanlinna theory to functional equations of the form , where , are meromorphic functions in , or in an “open disk”, satisfying conditions on the order of its zeros and poles. In various cases we show that and must be constant when they are meromorphic in all , or they must be quotients of bounded functions when they are meromorphic in an “open disk”. In particular,...
Approximation and interpolation of entire functions
Approximation and interpolation of entire functions and generalized orders
Approximation by transcendental polynomials
Approximation of entire functions of slow growth.
Approximation of entire functions of slow growth on compact sets
In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
Approximation of entire functions of two complex variables in Banach spaces.