Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Author: Nakahama, Ryosuke
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211982
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups. Ryosuke Nakahama. SIGMA 19 (2023), 049, 74 pages

Let (, ₁) = (, (σ)₀) be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces D₁ = ₁/₁ ⊂ D = /, realized as bounded symmetric domains in complex vector spaces p⁺₁ := (p⁺)σ ⊂ p⁺ respectively. Then the universal covering group ˜ of acts unitarily on the weighted B...