Basic Oka Theory in Several Complex Variables - Couverture souple

Noguchi, Junjiro

9789819720552: Basic Oka Theory in Several Complex Variables

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ISBN 10 : 9819720559 ISBN 13 : 9789819720552

Editeur : Springer, 2024

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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The nature of the present book is evinced by its approach following Oka’s unpublished five papers of 1943 with his guiding methodological principle termed the “Joku-Iko Principle”, where historically the Pseudoconvexity Problem (Hartogs, Levi)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 L2-∂-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 Poincar�’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.

Les informations fournies dans la section � Synopsis � peuvent faire r�f�rence � une autre �dition de ce titre.

� propos de l?auteur

The author is currently Professor Emeritus at The University of Tokyo and Tokyo Institute of Technology.

Les informations fournies dans la section � A propos du livre � peuvent faire r�f�rence � une autre �dition de ce titre.

�diteur: Springer
Date d'�dition: 2024
Langue: anglais
ISBN 10: 9819720559
ISBN 13: 9789819720552
Reliure: Broch�
Nombre de pages: 240
Coordonn�es du fabricant: Springer Nature Customer Service Center GmbH
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Basic Oka Theory in Several Complex Variables

Junjiro Noguchi

Edit� par Springer Nature Singapore Aug 2024, 2024

ISBN 10 : 9819720559 ISBN 13 : 9789819720552

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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 L2- -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 Poincar�'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. 221 pp. Englisch. N� de r�f. du vendeur 9789819720552

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Basic Oka Theory in Several Complex Variables

Noguchi, Junjiro

Edit� par Springer, Berlin|Springer Nature Singapore|Springer, 2024

ISBN 10 : 9819720559 ISBN 13 : 9789819720552

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 b. N� de r�f. du vendeur 1429714778

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Basic Oka Theory in Several Complex Variables

Junjiro Noguchi

Edit� par Springer Nature Singapore, Springer Nature Singapore Jul 2024, 2024

ISBN 10 : 9819720559 ISBN 13 : 9789819720552

Neuf Taschenbuch

Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne

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Taschenbuch. Etat : Neu. Neuware -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 Ok�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 L2-�-bar method, but yet reaches the core of the theory with the complete proofs.Two proofs for Levi�s Problem are provided: One is Ok�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 Poincar�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.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 240 pp. Englisch. N� de r�f. du vendeur 9789819720552

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Basic Oka Theory in Several Complex Variables

Junjiro Noguchi

Edit� par Springer Nature Singapore, Springer Nature Singapore, 2024

ISBN 10 : 9819720559 ISBN 13 : 9789819720552

Neuf Taschenbuch

Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 L2- -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 Poincar�'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. N� de r�f. du vendeur 9789819720552

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