Growth estimates for solutions of linear complex differential equations.
Growth numbers of Entire Functions Defined by Dirichlet Series
Growth of entire functions with some univalent Gelfond-Leontev derivatives.
Growth of (frequently) hypercyclic functions for differential operators
We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions for these functions on particular rays or sectors. Our research extends known results in several respects.
Growth of meromorphic solutions of higher-order linear differential equations.
Growth of solutions of a class of complex differential equations
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].
Growth of solutions of certain non-homogeneous linear differential equations with entire coefficients.
Growth of solutions of complex differential equations with coefficients of finite iterated order.
Growth of solutions of higher-order linear differential equations.
Growth of solutions to higher order linear homogeneous differential equations in angular domains.
Growth of solutions to linear differential equations with entire coefficients of slow growth.
Hausdorff convergence and the limit shape of the unicorns.
Hermite interpolation and an inequality for entire functions of exponential type.
Holomorphic extension of a function whose odd derivatives are summable
Holomorphic Functions with Mean p-valent Derivatives.
Holomorphic motions commuting with semigroups
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
Holomorphic solutions of an inhomogeneous Cauchy equation.
Horizontal sections of connections on curves and transcendence
Let K be a number field, X be a smooth projective curve over it and D be a reduced divisor on X. Let (E,∇) be a vector bundle with connection having meromorphic singularities on D. Let and (the ’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E-section of arithmetic type of the vector bundle E with respect to the points ; this is the natural generalization of the notion of E-function defined in Siegel-Shidlovskiĭ theory. We prove...
Hyperbolic components of polynomials with a fixed critical point of maximal order
Hyperbolic components of the complex exponential family
We describe the structure of the hyperbolic components of the parameter plane of the complex exponential family, as started in [1]. More precisely, we label each component with a parameter plane kneading sequence, and we prove the existence of a hyperbolic component for any given such sequence. We also compare these sequences with the more commonly used dynamical kneading sequences.