Batzorig Undrakh | Searcharxiv

arXiv2025

Finite-dimensional model spaces invariant under composition operators

Finite-dimensional model spaces are quotient spaces of the Hardy space on the open unit disc, determined by finite Blaschke products. Composition operators, on the other hand, act by composing Hardy space functions with analytic self-maps of the open unit disc. Both are classical and well-studied objects in the theory of analytic function spaces. In this paper, we present a complete characterization of finite-dimensional model spaces that are invariant under composition operators. Finite cyclic groups and the prime factorizations of natural numbers play a crucial role in understanding the structure of such invariant subspaces and the associated analytic self-maps.

math.FA↗

arXiv2018

Rational dilation problems associated with constrained algebras

It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is accomplished in part by finding a minimal set of test functions. In addition, an Agler-Pick interpolation theorem is given and it is proved that there exist Kaijser-Varopoulos style examples of non-contractive unital representations where the generators are contractions.

math.FA↗