Function theoretic aspects of the symmetrized polydisc and generalization

2026/08/01 by Sourav Pal, Nitin Tomar
Mathematics · #math.CV #math.FA #math.OA

paper · pdf

This is just a primary draft and a revised version will appear soon

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

We introduce Schur-Agler type class for the symmetrized polydisc \mathbbG_d and establish a realization theorem for functions in this class. We state and prove an interpolation theorem on \mathbbG_d with interpolating functions belonging to the associated Schur-Agler type class. Moreover, Toeplitz corona and extension theorems are established for \mathbbG_d. We also extend the realization, interpolation, Toeplitz corona and extension theorems to a more general symmetrized family of domains Θ_d.

Citations

• Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem
• Contractive Hilbert modules on quotient domains
• Complete Norm Preserving Extensions of Holomorphic Functions
• Interpolating sequences for the Banach algebras generated by a class of test functions
• Extension Property and Universal Sets
• Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk
• On the Nevanlinna problem -- Characterization of all Schur-Agler class solutions affiliated with a given kernel
• Realization of functions on the symmetrized bidisc
• Geodesics, retracts, and the norm-preserving extension property in the\n symmetrized bidisc
• Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting
• Agler interpolation families of kernels
• Test Functions, Kernels, Realizations and Interpolation
• Interpolation in Semigroupoid Algebras