عنوان	POLYNOMIALLY BOUNDED SOLUTIONS OF THE LOEWNER DIFFERENTIAL EQUATION IN SEVERAL COMPLEX
نوع پژوهش	مقاله چاپ شده
کلیدواژه‌ها	Biholomorphic mapping, Loewner differential equation, poly- nomially bounded, subordination chain, parametric representation.
چکیده	We determine the form of polynomially bounded solutions to the Loewner differential equation that is satis ed by univalent subordi- nation chains of the form f(z; t) = e ∫ t 0 A()d z + , where A : [0;1] ! L(Cn;Cn) is a locally Lebesgue integrable mapping and satisfying the condition sup s0 ∫ 1 0 exp {∫ t s [A() 􀀀 2m(A())In]d } dt < 1; and m(A(t)) > 0 for t  0, where m(A) = minfRe ⟨A(z); z⟩ : ∥z∥ = 1g. We also give sufficient conditions for g(z; t) = M(f(z; t)) to be polynomi- ally 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. Keywords: Biholomorphic
پژوهشگران	سمیرا رهروی (نفر دوم)، علی عبادیان (نفر اول)، سعید شمس (نفر سوم)، Janusz Sokol (نفر چهارم)