Commuting tuple of multiplication operators homogeneous under the unitary group
Soumitra Ghara,
Surjit Kumar,
Gadadhar Misra
et al.
Abstract:Let be the group of unitary matrices. We find conditions to ensure that a ‐homogeneous ‐tuple is unitarily equivalent to multiplication by the coordinate functions on some reproducing kernel Hilbert space , . We describe this class of ‐homogeneous operators, equivalently, nonnegative kernels quasi‐invariant under the action of . We classify quasi‐invariant kernels transforming under with two specific choice of multipliers. A crucial ingredient of the proof is that the group has exactly two inequivalent … Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.