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PROPER HOLOMORPHIC MAPPINGS, POSITIVITY CONDITIONS, AND ISOMETRIC IMBEDDING
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 Title & Authors
PROPER HOLOMORPHIC MAPPINGS, POSITIVITY CONDITIONS, AND ISOMETRIC IMBEDDING
D`Angelo, John P.;
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 Abstract
This article discusses in detail how the study of proper holomorphic rational mappings between balls in different dimensions relates to positivity conditions and to isometric imbedding of holomorphic bundles. The first chapter discusses rational proper mappings between balls; the second chapter discusses seven distinct positivity conditions for real-valued polynomials in several complex variables; the third chapter reveals how these issues relate to an isometric imbedding theorem for holomorphic vector bundles proved by the author and Catlin.
 Keywords
proper holomorphic mappings;unit ball;positivity conditions;Hermitian forms;holomorphic line bundles;isometric imbedding;CR mappings;
 Language
English
 Cited by
1.
HERMITIAN COMPLEXITY OF REAL POLYNOMIAL IDEALS, International Journal of Mathematics, 2012, 23, 06, 1250026  crossref(new windwow)
2.
COMPLEX VARIABLES ANALOGUES OF HILBERT'S SEVENTEENTH PROBLEM, International Journal of Mathematics, 2005, 16, 06, 609  crossref(new windwow)
3.
Uniqueness of certain polynomials constant on a line, Linear Algebra and its Applications, 2010, 433, 4, 824  crossref(new windwow)
4.
COMPLEXITY RESULTS FOR CR MAPPINGS BETWEEN SPHERES, International Journal of Mathematics, 2009, 20, 02, 149  crossref(new windwow)
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