# Infinitesimal generators of semigroups with prescribed boundary fixed points

Infinitesimal generators of semigroups with prescribed boundary fixed points We study infinitesimal generators of one-parameter semigroups in the unit disk D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {D}$$\end{document} having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein–Milman Theory we obtain new sharp inequalities relating spectral values at the fixed points with other important quantities having dynamical meaning. We also give a new proof of the classical Cowen–Pommerenke inequalities for univalent self-maps of D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {D}$$\end{document}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Infinitesimal generators of semigroups with prescribed boundary fixed points

, Volume 10 (3) – Aug 8, 2020
38 pages

/lp/springer-journals/infinitesimal-generators-of-semigroups-with-prescribed-boundary-fixed-ElYAVH0myo
Publisher
Springer Journals
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-020-00378-z
Publisher site
See Article on Publisher Site

### Abstract

We study infinitesimal generators of one-parameter semigroups in the unit disk D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {D}$$\end{document} having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein–Milman Theory we obtain new sharp inequalities relating spectral values at the fixed points with other important quantities having dynamical meaning. We also give a new proof of the classical Cowen–Pommerenke inequalities for univalent self-maps of D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {D}$$\end{document}.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Aug 8, 2020