Polynomially bounded solutions to the Loewner differential equation in several complex variables
نویسندگان
چکیده
منابع مشابه
Polynomially bounded solutions of the Loewner differential equation in several complex variables
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$, where $A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [A(tau)...
متن کاملpolynomially bounded solutions of the loewner differential equation in several complex variables
we determine the form of polynomially bounded solutions to the loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t a(tau){rm d}tau}z+cdots$, where $a:[0,infty]rightarrow l(mathbb{c}^n,mathbb{c}^n)$ is a locally lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [a(tau)...
متن کاملThe Loewner Differential Equation and Slit Mappings
In his study of extremal problems for univalent functions, K. Löwner [11] (who later changed his name into C. Loewner) introduced the differential equation named after him. It was a key ingredient in the proof of the Bieberbach conjecture by de Branges [2]. It was used by L. Carleson and N. Makarov in their investigation of a process similar to DLA [3]. Recently, O. Schramm [20] found a descrip...
متن کاملPower Bounded Composition Operators in Several Variables
Let φ be an analytic self-map of the open unit polydisk D , N ∈ N. Such a map induces a composition operator Cφ acting on weighted Banach spaces of holomorphic functions. We study when such operators are power bounded resp. uniformly mean ergodic. Mathematics Subject Classification (2010): 47B33, 47B38
متن کاملSome inequalities in connection to relative orders of entire functions of several complex variables
Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.02.080