مشخصات پژوهش

صفحه نخست /POLYNOMIALLY BOUNDED ...
عنوان POLYNOMIALLY BOUNDED SOLUTIONS OF THE LOEWNER DIFFERENTIAL EQUATION IN SEVERAL COMPLEX VARIABLES
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها Biholomorphic mapping, Loewner differential equation, polynomially bounded, subordination chain, parametric representation.
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 ∫ t 0 A(τ)dτ z + · · · , where A : [0,∞] → L(Cn, Cn) is a locally Lebesgue integrable mapping and satisfying the condition sup s≥0 ∫ ∞ 0 exp {∫ t s [A(τ) − 2m(A(τ))In]dτ } dt < ∞, and m(A(t)) > 0 for t ≥ 0, where m(A) = min{Re ⟨A(z), z⟩ : ∥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
پژوهشگران سمیرا رهروی (نفر دوم)، علی عبادیان (نفر اول)، سعید شمس (نفر سوم)، Janusz Sokol (نفر چهارم)