Basic Oka Theory in Several Complex Variables
-
- Taschenbuch ausgewählt
- eBook
-
Sprache:Englisch
54,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
20.07.2024
Abbildungen
XVI, 221 p. 22 illus., 5 illus. in color.
Verlag
Springer SingaporeSeitenzahl
221
Maße (L/B/H)
23,5/15,5/1,4 cm
Gewicht
371 g
Auflage
2024
Sprache
Englisch
ISBN
978-981-9720-55-2
This book provides a new, comprehensive, and self-contained account of Oka theory as an introduction to function theory of several complex variables, mainly concerned with the Three Big Problems (Approximation, Cousin, Pseudoconvexity) that were solved by Kiyoshi Oka and form the basics of the theory. The purpose of the volume is to serve as a textbook in lecture courses right after complex function theory of one variable. The presentation aims to be readable and enjoyable both for those who are beginners in mathematics and for researchers interested in complex analysis in several variables and complex geometry.
The nature of the present book is evinced by its approach following Oka’s unpublished five papers of 1943 with his guiding methodological principle termed the “Joku-Iko Principle”, where historically the Pseudoconvexity Problem (Hartogs, Levi) was first solved in all dimensions, even for unramified Riemann domains as well.
The method that is used in the book is elementary and direct, not relying on the cohomology theory of sheaves nor on the
L
2-∂-bar method, but yet reaches the core of the theory with the complete proofs.
Two proofs for Levi’s Problem are provided: One is Oka’s original with the Fredholm integral equation of the second kind combined with the Joku-Iko Principle, and the other is Grauert’s by the well-known “bumping-method” with L. Schwartz’s Fredholm theorem, of which a self-contained, rather simple and short proof is given. The comparison of them should be interesting even for specialists.
In addition to the Three Big Problems, other basic material is dealt with, such as Poincaré’s non-biholomorphism between balls and polydisks, the Cartan–Thullen theorem on holomorphic convexity, Hartogs’ separate analyticity, Bochner’s tube theorem, analytic interpolation, and others.
It is valuable for students and researchers alike to look into the original works of Kiyoshi Oka, which are not easy to find in books or monographs.
Ein neues Kapitel für Ihre Bücher
Ein neues Kapitel für Ihre Bücher
Schenken Sie Ihren alten Schätzen ein zweites Leben und erhalten Sie dafür eine Thalia Geschenkkarte.
Noch keine Bewertungen vorhanden
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.
Kurze Frage zu unserer Seite
Vielen Dank für Ihr Feedback
Wir nutzen Ihr Feedback, um unsere Produktseiten zu verbessern. Bitte haben Sie Verständnis, dass wir Ihnen keine Rückmeldung geben können. Falls Sie Kontakt mit uns aufnehmen möchten, können Sie sich aber gerne an unseren Kund*innenservice wenden.
zum Kundenservice