polynomially bounded solutions of the loewner differential equation in several complex variables
نویسندگان
چکیده
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 $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [a(tau)-2m(a(tau))i_n]rm {d}tauright}right|{rm d}t0$ for $tgeq0$, where $m(a)=min{mathfrak{re}leftlangle a(z),zrightrangle:|z|=1}$. we also give sufficient conditions for $g(z,t)=m(f(z,t))$ to be polynomially bounded, where $f(z,t)$ is an $a(t)$-normalized polynomially bounded loewner chain solution to the loewner differential equation and $m$ is an entire function. on the other hand, we show that all $a(t)$-normalized polynomially bounded solutions to the loewner differential equation are loewner chains.
منابع مشابه
Polynomially bounded solutions of the Loewner differential equation in several complex variables
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$, where $A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [A(tau)...
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۳، صفحات ۵۲۱-۵۳۷
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