اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBoundary behavior of infinitesimal generators in the unit ball
121
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove a Julia-Wolff-Caratheodory type theorem for infinitesimal generators on the unit ball in C^n. Moreover, we study jets expansions at the boundary and give necessary and sufficient conditions on such jets for an infinitesimal generator to generate a group of automorphisms of the ball.
قيم البحث
اقرأ أيضاً
We study infinitesimal generators of one-parameter semigroups in the unit disk $mathbb D$ having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein-Milman Theory we ob
tain new sharp inequalities relating spectral values at the fixed points with other important quantities having dynamical meaning.vWe also give a new proof of the classical Cowen-Pommerenke inequalities for univalent self-maps of $mathbb D$.
We study proper rational maps from the unit disk to balls in higher dimensions. After gathering some known results, we study the moduli space of unitary equivalence classes of polynomial proper maps from the disk to a ball, and we establish a normal
form for these equivalence classes. We also prove that all rational proper maps from the disk to a ball are homotopic in target dimension at least $2$.
We study almost sure separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0-1 Komolgorov law for a sequence to be interpolating almost surely for all the Besov-Sobolev spaces $
B_{2}^{sigma}left(mathbb{B}_{d}right)$, in the range $0 < sigmaleq1 / 2$. For those spaces, such interpolating sequences coincide with interpolating sequences for their multiplier algebras, thanks to the Pick property. This is not the case for the Hardy space $mathrm{H}^2(mathbb{D}^d)$ and its multiplier algebra $mathrm{H}^infty(mathbb{D}^d)$: in the polydisc, we obtain a sufficient and a necessary condition for a sequence to be $mathrm{H}^infty(mathbb{D}^d)$-interpolating almost surely. Those two conditions do not coincide, due to the fact that the deterministic starting point is less descriptive of interpolating sequences than its counterpart for the unit ball. On the other hand, we give the $0-1$ law for random interpolating sequences for $mathrm{H}^2(mathbb{D}^d)$.
We present a rigidity property of holomorphic generators on the open unit ball $mathbb{B}$ of a Hilbert space $H$. Namely, if $finHol (mathbb{B},H)$ is the generator of a one-parameter continuous semigroup ${F_t}_{tgeq 0}$ on $mathbb{B}$ such that fo
r some boundary point $tauin partialmathbb{B}$, the admissible limit $K$-$limlimits_{ztotau}frac{f(x)}{|x-tau|^{3}}=0$, then $f$ vanishes identically on $mathbb{B}$.
We prove a theorem on separation of boundary null points for generators of continuous semigroups of holomorphic self-mappings of the unit disk in the complex plane. Our construction demonstrates the existence and importance of a particular role of th
e binary operation $circ$ given by $1 / f circ g = 1/f + 1/g$ on generators.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
