اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAbel averages and holomorphically pseudo-contractive maps in Banach spaces
239
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A class of maps in a complex Banach space is studied, which includes both unbounded linear operators and nonlinear holomorphic maps. The defining property, which we call {sl pseudo-contractivity}, is introduced by means of the Abel averages of such maps. We show that the studied maps are dissipative in the spirit of the classical Lumer-Phillips theorem. For pseudo-contractive holomorphic maps, we establish the power convergence of the Abel averages to holomorphic retractions.
قيم البحث
اقرأ أيضاً
In this paper we introduce a class of pseudo-dissipative holomorphic maps which contains, in particular, the class of infinitesimal generators of semigroups of holomorphic maps on the unit ball of a complex Banach space. We give a growth estimate for
maps of this class. In particular, it follows that pseudo-dissipative maps on the unit ball of (infinite-dimensional) Banach spaces are bounded on each domain strictly contained inside the ball. We also present some applications.
Let $mathcal{G}$ resp. $M$ be a positive dimensional Lie group resp. connected complex manifold without boundary and $V$ a finite dimensional $C^{infty}$ compact connected manifold, possibly with boundary. Fix a smoothness class $mathcal{F}=C^{infty}
$, Holder $C^{k, alpha}$ or Sobolev $W^{k, p}$. The space $mathcal{F}(V, mathcal{G})$ resp. $mathcal{F}(V, M)$ of all $mathcal{F}$ maps $V to mathcal{G}$ resp. $V to M$ is a Banach/Frechet Lie group resp. complex manifold. Let $mathcal{F}^0(V, mathcal{G})$ resp. $mathcal{F}^{0}(V, M)$ be the component of $mathcal{F}(V, mathcal{G})$ resp. $mathcal{F}(V, M)$ containing the identity resp. constants. A map $f$ from a domain $Omega subset mathcal{F}_1(V, M)$ to $mathcal{F}_2(W, M)$ is called range decreasing if $f(x)(W) subset x(V)$, $x in Omega$. We prove that if $dim_{mathbb{R}} mathcal{G} ge 2$, then any range decreasing group homomorphism $f: mathcal{F}_1^0(V, mathcal{G}) to mathcal{F}_2(W, mathcal{G})$ is the pullback by a map $phi: W to V$. We also provide several sufficient conditions for a range decreasing holomorphic map $Omega$ $to$ $mathcal{F}_2(W, M)$ to be a pullback operator. Then we apply these results to study certain decomposition of holomorphic maps $mathcal{F}_1(V, N) supset Omega to mathcal{F}_2(W, M)$. In particular, we identify some classes of holomorphic maps $mathcal{F}_1^{0}(V, mathbb{P}^n) to mathcal{F}_2(W, mathbb{P}^m)$, including all automorphisms of $mathcal{F}^{0}(V, mathbb{P}^n)$.
We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the domain yie
lds a new domain which also is a John domain. We apply this result to prove the stability of the inner uniform domains. Finally, we consider a wider class of domains, so called $psi$-John domains and prove a similar result for this class.
In this paper we develop a stochastic integration theory for processes with values in a quasi-Banach space. The integrator is a cylindrical Brownian motion. The main results give sufficient conditions for stochastic integrability. They are natural ex
tensions of known results in the Banach space setting. We apply our main results to the stochastic heat equation where the forcing terms are assumed to have Besov regularity in the space variable with integrability exponent $pin (0,1]$. The latter is natural to consider for its potential application to adaptive wavelet methods for stochastic partial differential equations.
In this paper we study the compactness of operators on the Bergman space of the unit ball and on very generally weighted Bargmann-Fock spaces in terms of the behavior of their Berezin transforms and the norms of the operators acting on reproducing ke
rnels. In particular, in the Bergman space setting we show how a vanishing Berezin transform combined with certain (integral) growth conditions on an operator $T$ are sufficient to imply that the operator is compact. In the weighted Bargmann-Fock space setting we show that the reproducing kernel thesis for compactness holds for operators satisfying similar growth conditions. The main results extend the results of Xia and Zheng to the case of the Bergman space when $1 < p < infty$, and in the weighted Bargmann-Fock space setting, our results provide new, more general conditions that imply the work of Xia and Zheng via a more familiar approach that can also handle the $1 < p < infty$ case.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
