Corona problems in spaces of entire functions with growth conditions

1987 ◽  
Vol 9 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Graziano Gentili ◽  
Daniele Struppa
Keyword(s):  
Entire Functions ◽  
Growth Conditions

scholarly journals Dynamics of entire functions near the essential singularity

1986 ◽  
Vol 6 (4) ◽  
pp. 489-503 ◽  
Author(s):  
Robert L. Devaney ◽  
Folkert Tangerman
Keyword(s):  
Entire Functions ◽  
Julia Set ◽  
Julia Sets ◽  
Growth Conditions ◽  
Cantor Set ◽  
Essential Singularity ◽  
Shift Automorphism

AbstractWe show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

ENTIRE FUNCTIONS SHARING ARGUMENTS OF INTEGRALITY, I

2009 ◽  
Vol 05 (02) ◽  
pp. 339-353 ◽  
Author(s):  
JONATHAN PILA
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Weak Form ◽  
Growth Conditions ◽  
Real Numbers

Let f be an entire function that is real and strictly increasing for all sufficiently large real arguments, and that satisfies certain additional conditions, and let Xf be the set of non-negative real numbers at which f is integer valued. Suppose g is an entire function that takes integer values on Xf. We find growth conditions under which f,g must be algebraically dependent (over ℤ) on X. The result generalizes a weak form of a theorem of Pólya.

scholarly journals Holomorphic functions, relativistic sum, Blaschke products and superoscillations

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Stefano Pinton ◽  
Irene Sabadini
Keyword(s):  
Infinite Order ◽  
Complex Analysis ◽  
Differential Operators ◽  
Entire Functions ◽  
Growth Conditions ◽  
Weak Values ◽  
Blaschke Products ◽  
Independent Field ◽  
Superoscillating Functions ◽  
Band Limited

AbstractSuperoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The notion of superoscillation is a particular case of that one of supershift. In the recent years, superoscillating functions, that appear for example in weak values in quantum mechanics, have become an interesting and independent field of research in complex analysis and in the theory of infinite order differential operators. The aim of this paper is to study some infinite order differential operators acting on entire functions which naturally arise in the study of superoscillating functions. Such operators are of particular interest because they are associated with the relativistic sum of the velocities and with the Blaschke products. To show that some sequences of functions preserve the superoscillatory behavior it is of crucial importance to prove that their associated infinite order differential operators act continuously on some spaces of entire functions with growth conditions.

Interpolation in Spaces of Entire Functions in ℂN

1976 ◽  
Vol 19 (1) ◽  
pp. 109-112 ◽  
Author(s):  
Lawrence Gruman
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Growth Conditions ◽  
Set Of Points

Let {sm} be a discrete set of points in ℂN and λm any sequence of points in ℂ. We shall be interested in finding an entire function F(z) such that F(sm)=λm. This is of course easy if no restriction is placed on F, but we shall be interested in finding an F which in addition satisfies certain growth conditions.We shall denote the variable z=(z1,..., zN), zj=xj+iyj,

Influence of MBE Growth Conditions on Dislocation Densities of GaAs/Ge Epilayers Grown on Silicon Substrates

1985 ◽  
Vol 43 ◽  
pp. 364-365
Author(s):  
K.M. Hones ◽  
P. Sheldon ◽  
B.G. Yacobi ◽  
A. Mason
Keyword(s):  
High Efficiency ◽  
Lattice Mismatch ◽  
Low Cost ◽  
Growth Conditions ◽  
Nonradiative Recombination ◽  
Device Structure ◽  
Si Substrates ◽  
Transmission Electron ◽  
Dislocation Densities ◽  
Dislocation Type

There is increasing interest in growing epitaxial GaAs on Si substrates. Such a device structure would allow low-cost substrates to be used for high-efficiency cascade- junction solar cells. However, high-defect densities may result from the large lattice mismatch (∼4%) between the GaAs epilayer and the silicon substrate. These defects can act as nonradiative recombination centers that can degrade the optical and electrical properties of the epitaxially grown GaAs. For this reason, it is important to optimize epilayer growth conditions in order to minimize resulting dislocation densities. The purpose of this paper is to provide an indication of the quality of the epitaxially grown GaAs layers by using transmission electron microscopy (TEM) to examine dislocation type and density as a function of various growth conditions. In this study an intermediate Ge layer was used to avoid nucleation difficulties observed for GaAs growth directly on Si substrates. GaAs/Ge epilayers were grown by molecular beam epitaxy (MBE) on Si substrates in a manner similar to that described previously.

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