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020 _a9789819720569
_9978-981-97-2056-9
024 7 _a10.1007/978-981-97-2056-9
_2doi
050 4 _aQA331.7
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
100 1 _aNoguchi, Junjiro.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980947
245 1 0 _aBasic Oka Theory in Several Complex Variables
_h[electronic resource] /
_cby Junjiro Noguchi.
250 _a1st ed. 2024.
264 1 _aSingapore :
_bSpringer Nature Singapore :
_bImprint: Springer,
_c2024.
300 _aXVI, 221 p. 22 illus., 5 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x2191-6675
505 0 _a1 Holomorphic Functions -- 2 Coherent Sheaves and Oka’s Joku-Iko Principle -- 3 Domains of Holomorphy -- 4 Pseudoconvex Domains I — Problem and Reduction -- 5 Pseudoconvex Domains II — Solution.
520 _aThis 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 The nature of the present book is evinced by its approach following Oka’s unpublished five papers of 1943 with his guiding methodological principle termed the “Joku-Iko Principle”, where historically the Pseudoconvexity Problem (Hartogs, Levi)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 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.
650 0 _aFunctions of complex variables.
_972222
650 0 _aAlgebra.
_91501
650 0 _aTopology.
_972917
650 1 4 _aSeveral Complex Variables and Analytic Spaces.
_972225
650 2 4 _aAlgebra.
_91501
650 2 4 _aTopology.
_972917
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9789819720552
776 0 8 _iPrinted edition:
_z9789819720576
830 0 _aUniversitext,
_x2191-6675
_973095
856 4 0 _uhttps://doi.org/10.1007/978-981-97-2056-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61771
_d61771