Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem

2025/05/29 by Jain, Shubham, Kumar, Surjit, Mal, Milan Kumar +1
#47A13 #47A56 #47A57 #47B32 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 32A70 #Secondary 46E22

paper · doi:10.48550/arxiv.2505.23492

Abstract

We introduce a Schur-Agler type class associated with the tetrablock and establish a realization theorem for this class. Furthermore, we provide a tetrablock analog of the interpolation theorem, extension theorem, and the Toeplitz corona theorem.

Citations

• A transference principle for involution-invariant functional Hilbert spaces
• Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk
• Realization of functions on the symmetrized bidisc
• Interpolation and transfer-function realization for the noncommutative Schur-Agler class
• Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc
• Test Functions, Kernels, Realizations and Interpolation
• Interpolation in Semigroupoid Algebras

Related

• Brown-Halmos type characterization for the tetrablock
• Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk
• Holomorphic functions on the symmetrized bidisk II -- Interpolating sequences and the Toeplitz corona theorem
• A note on the dilation of a certain family of tetrablock contractions
• Truncated Toeplitz operators and the Agler-Young class