Analysis and Geometry on Complex Homogeneous Domains: 185 - Brossura

Faraut, Jacques; Kaneyuki, Soji; Koranyi, Adam; Lu, Qi-keng; Roos, Guy

Brossura

ISBN 10: 1461271150 ISBN 13: 9781461271154

Casa editrice: Birkhäuser, 2012

Riassunto

[see attached] This excellent introductory text covers a number of important areas in complex analysis and geometry. Written by experts in their respective fields, each of the five chapters unfolds from the basics to the more complex. Unlike other more laborious introductory texts, the exposition here is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. Topics covered include: function spaces on complex semigroups * graded Lie algebras, related geometric structures, and pseudo- Hermitian symmetric spaces * function spaces on bounded symmetric

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Recensione

"The book is clearly an important contribution to the literature on the subject. A number of results presented here is not accessible in book form elsewhere. Both research students and professional mathematicians will find this valuable volume an extremely useful guide and reference work."

--Publicationes Mathematicae

"This book, which is a useful text for advanced graduate students and researchers...gives a comprehensive account of the field of homogeneous complex domains...The exposition is rapidly paced and efficient, without compromising proofs. Moreover, plenty of examples are given, enabling the reader to understand the essential ideas behind the notions and the theorems."

--ZAA

"This book has been written by five outstanding experts with the intention of surveying the most important goals and viewpoints of the field...It is a pleasant reading, details of proofs are supplied or omitted in a very well chosen manner...Many new top results are described and it contains the most important references after each part. I recommend it first of all since, using this book, one can reach the research level with considerably less effort than by the aid of other means of the recent literature."

--ASM

Contenuti

I Function Spaces on Complex Semi-groups by Jacques Faraut.- I Hilbert Spaces of Holomorphic Functions.- I.1 Reproducing kernels.- I.2 Invariant Hilbert spaces of holomorphic functions..- II Invariant Cones and Complex Semi-groups.- II.1 Complex semi-groups.- 1I.2 Invariant cones in a representation space.- II.3 Invariant cones in a simple Lie algebra.- III Positive Unitary Representations.- III.1 Self-adjoint operators.- III.2 Unitary representations.- III.3 Positive unitary representations.- IV Hilbert Function Spaces on Complex Semi-groups.- IV.1 Schur orthogonality relations.- IV.2 The Hardy space of a complex semi-group.- IV.3 The Cauchy-Szegö kernel and the Poisson kernel.- IV.4 Spectral decomposition of the Hardy space.- V Hilbert Function Spaces on SL(2,?).- V.1 Complex Olshanski semi-group in SL(2,?).- V.2 Irreducible positive unitary representations.- V.3 Characters and formal dimensions of the representations ?m.- V.4 Bi-invariant Hilbert spaces of holomorphic functions.- V.5 The Hardy space.- V.6 The Bergman space.- VI Hilbert Function Spaces on a Complex Semi-simple Lie Group.- VI.1 Bounded symmetric domains.- VI.2 Irreducible positive unitary representations.- VI.3 Characters and formal dimensions.- VI.4 Bi-invariant Hilbert spaces of holomorphic functions.- References.- II Graded Lie Algebras and Pseudo-hermitian Symmetric Spaces by Soji Kaneyuki.- I Semisimple Graded Lie Algebras.- I.1 Root theory of real semisimple Lie algebras.- I.2 Semisimple graded Lie algebras.- I.3 Example.- I.4 Tables.- II Symmetric R-Spaces.- II.1 Symmetric R-spaces and their noncompact duals.- II.2 Sylvester’s law of inertia in simple GLA’s.- II.3 Generalized conformal structures and causal structures.- III Pseudo-Hermitian Symmetric Spaces.- III.1 Pseudo-Hermitian spaces and nonconvex Siegel domains.- III.2 Simple reducible pseudo-Hermitian symmetric spaces.- References.- III Function Spaces on Bounded Symmetric Domains by Adam Kordnyi.- I Bergman Kernel and Bergman Metric.- I.1 Domains in Cr“.- 1.2 Bergman kernel, reproducing kernels.- I.3 The Bergman metric.- II Symmetric Domains and Symmetric Spaces.- II.1 Basic facts, definitions.- II.2 Riemannian symmetric spaces.- II.3 Theory of oiLa’s.- II.4 OiLa’s of bounded symmetric domains.- II.5 Cartan subalgebras.- III Construction of the Hermitian Symmetric Spaces.- III.1 The Borel imbedding theorem.- III.2 The Harish-Chandra realization.- III.3 Remarks on classification.- IV Structure of Symmetric Domains.- IV.1 Restricted root system, boundary orbits.- IV.2 Decomposition under the Cayley transform.- V The Weighted Bergman Spaces.- V.1 Analysis on symmetric domains.- V.2 Decomposition under K.- V.3 Spaces of holomorphic functions.- VI Differential Operators.- VI.1 Properties of ?s.- VI.2 Invariant differential operators on ?.- VI.3 Further results on $$ \mathbb{D}$$(?).- VI.4 Extending D? to p+.- VII Function Spaces.- VII.1 The holomorphic discrete series.- VII.2 Analytic continuation of the holomorphic discrete series.- VII.3 Explicit formulas for the inner products.- VII.4 L9–spaces and Bergman type projections.- VII.5 Some questions of duality.- VII.6 Further results.- References.- IV The Heat Kernels of Non Compact Symmetric Spaces by Qi-keng Lu.- I Introduction.- II The Laplace-Beltrami Operator in Various Coordinates.- III The Integral Transformations.- IV The Heat Kernel of the Hyperball R?(m, n).- V The Harmonic Forms on the Complex Grassmann Manifold.- VI The Horo-hypercircle Coordinate of a Complex Hyperball.- VII The Heat Kernel of RII(m).- VIII The Matrix Representation of NIRGSS.- References.- V Jordan Triple Systems by Guy Roos.- I Polynomial Identities.- I.1 Definition of Jordan triple systems.- I.2 Identities of minimal degree.- 1.3 Jordan representations and duality.- 1.4 The fundamental identity of degree 7.- 1.5 The Bergman operator.- II Jordan Algebras.- II.1 Jordan algebras arising from a JTS.- II.2 Identities in a Jordan algebra.- II.3 The JTS associated to a Jordan algebra.- III The Quasi-inverse.- III.1 Quasi-invertibility in a Jordan algebra.- 111.2 Quasi-invertibility in a JTS.- 11I.3 Identities for the quasi-inverse.- 1II.4 Differential equations.- 1I1.5 Addition formulas.- IV The Generic Minimal Polynomial.- IV.1 Unital Jordan algebras.- IV.2 General Jordan algebras.- IV.3 Jordan triple systems.- V Tripotents and Peirce Decomposition.- V.1 Tripotent elements.- V.2 Peirce decomposition.- V.3 Orthogonality of tripotents.- V.4 Simultaneous Peirce decomposition.- VI Hermitian Positive JTS.- VI.1 Positivity.- VI.2 Spectral decomposition.- VI.3 Automorphisms.- VI.4 The spectral norm.- VI.5 Classification of Hermitian positive JTS.- VII Further Results and Open Problems.- VII.1 Schmid decomposition.- VII.2 Compactification of an hermitian positive JTS.- VII.3 Projective imbedding.- VII.4 Volume computations.- VII.5 Some open problems.- References.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461271150
• ISBN 13: 9781461271154
• Rilegatura: Copertina flessibile
• Numero di pagine: 560
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania