Einige elementare Ungleichungen für Exponentialpolynome.
Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes
Entire curves in complements of Cartesian products in .
Entire functions represented by Dirichlet series of two complex variables
Exponential polynomials and -modules
Extension of Entire Functions with Controlled Growth.
Extension sets for real analytic functions and applications to Radon transforms.
Formules de Jensen en plusieurs variables et applications arithmétiques
Generalized order and best approximation of entire function in -norm.
Geometry of the locus of polynomials of degree 4 with iterative roots
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
Growth properties of analytic and plurisubharmonic functions of finite order.
Growth properties of entire functions depending on a parameter
We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.
Holomorphy types on a Banach spaces
Interpolating discrete multiplicity varieties for
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Interpolating varieties for weighted spaces of entire functions in Cn.
We prove in this paper that a given discrete variety V in Cn is an interpolating variety for a weight p if and only if V is a subset of the variety {ξ ∈ Cn: f1(ξ) = f2(ξ) = ... = fn(ξ) = 0} of m functions f1, ..., fm in the weighted space the sum of whose directional derivatives in absolute value is not less than ε exp(-Cp(ζ)), ζ ∈ V for some constants ε, C > 0. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of f1, ..., fm. As a corollary, we solve...
Interpolation problems in cones. Nota I
In questa nota, si studiano problemi di interpolazione per varietà discrete in spazi di funzioni olomorfe in coni. In particolare si mostra come sia possibile estendere il Principio Fondamentale di Ehrenpreis ad equazioni di convoluzione nella spazio , introdotto in [4] in connessione con problemi di fisica quantistica.
Interpolation problems in cones. Nota II
Si estendono qui i risultati della nota precedente al caso di varietà non discrete. Ciò viene utilizzato per ottenere un teorema di rappresentazione per soluzioni di sistemi di equazioni di convoluzione in spazi di funzioni olomorfe in coni.
Liouville type theorem for solutions of linear partial differential equations with constant coefficients
We discuss existence of global solutions of moderate growth to a linear partial differential equation with constant coefficients whose total symbol P(ξ) has the origin as its only real zero. It is well known that for such equations, global solutions tempered in the sense of Schwartz reduce to polynomials. This is a generalization of the classical Liouville theorem in the theory of functions. In our former work we showed that for infra-exponential growth the corresponding assertion is true if and...
Meilleures estimations possibles pour l'ensemble des points algébriques de fonctions analytiques.
Non-extendable holomorphic functions of bounded growth in Reinhardt domains