Dissipative Holomorphic Functions, Bloch Radii, and the Schwarz Lemma

نویسندگان

  • Lawrence A. Harris
  • Simeon Reich
  • David Shoikhet
چکیده

The Hille-Yosida and Lumer-Phillips theorems play an important role in the theory of linear operators and its applications to evolution equations, probability and ergodic theory. (See, for example, [17] and [9].) Different nonlinear generalizations and analogues of these theorems can be found, for instance, in [13] and [2]. We are interested in establishing analogues of these theorems for the class of holomorphic functions which we view as a natural extension of the class of continuous linear operators. An analogue of the Hille-Yosida theorem for holomorphic functions was given in [14]. See also [15, 1]. Also, certain versions of the Hille-Yosida theorem as well as the Lumer-Phillips theorem were presented for nonlinear continuous operators in

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Two Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane

Introduction In this paper, we intend to show that without any certain growth condition on the weight function, we always able to present a weighted sup-norm on the upper half plane in terms of weighted sup-norm on the unit disc and supremum of holomorphic functions on the certain lines in the upper half plane. Material and methods We use a certain transform between the unit dick and the uppe...

متن کامل

Free Holomorphic Functions on the Unit Ball Of

In this paper we continue the study of free holomorphic functions on the noncommutative ball [B(H)]1 := n (X1, . . . , Xn) ∈ B(H) n : ‖X1X ∗ 1 + · · ·+ XnX ∗ n‖ 1/2 < 1 o , where B(H) is the algebra of all bounded linear operators on a Hilbert space H, and n = 1, 2, . . . or n = ∞. Several classical results from complex analysis have free analogues in our noncommutative setting. We prove a maxi...

متن کامل

Finsler Geometry of Holomorphic Jet Bundles

Introduction 107 1. Holomorphic Jet Bundles 113 2. Chern Classes and Cohomology Groups: The Case of Curves 120 3. Computation of Chern Classes: The Case of Surfaces 139 4. Finsler Geometry of Projectivized Vector Bundles 148 5. Weighted Projective Spaces and Projectivized Jet Bundles 153 6. The Lemma of Logarithmic Derivatives and the Schwarz Lemma 164 7. Surfaces of General Type 173 Acknowledg...

متن کامل

A special subspace of weighted spaces of holomorphic functions on the upper half plane

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

متن کامل

Classification of Invariant Fatou Components for Dissipative Hénon Maps

Fatou components for rational functions in the Riemann sphere are very well understood and play an important role in our understanding of one-dimensional dynamics. In higher dimensions the situation is less well understood. In this work we give a classification of invariant Fatou components for moderately dissipative Hénon maps. Most of our methods apply in a much more general setting. In parti...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000