Finite-dimensional model spaces invariant under composition operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909796850991104 |
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| author | Muthukumar, P. Sarkar, Jaydeb Undrakh, Batzorig |
| author_facet | Muthukumar, P. Sarkar, Jaydeb Undrakh, Batzorig |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_09666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-dimensional model spaces invariant under composition operators Muthukumar, P. Sarkar, Jaydeb Undrakh, Batzorig Functional Analysis Complex Variables Group Theory Operator Algebras 47B33, 30H10, 30J10, 46E15, 47A15, 20C05 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. |
| title | Finite-dimensional model spaces invariant under composition operators |
| topic | Functional Analysis Complex Variables Group Theory Operator Algebras 47B33, 30H10, 30J10, 46E15, 47A15, 20C05 |
| url | https://arxiv.org/abs/2507.09666 |