2024/05/30 by Yuxia Liang, Liang, Yuxia, J. R. Partington +1
Computer Science · Mathematics · #30H10 #47A15 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2405.19875
openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, it was shown that the image of a Toeplitz kernel of dimension greater than 1 under composition by an inner function is nearly S^*-invariant if and only if the inner function is an automorphism. Building on this, we determine the minimal Toeplitz kernel containing the image of a Toeplitz kernel under a composition operator with a general inner symbol, and extend this to weighted composition operators. Specifically, the corresponding cases for minimal model spaces are also given, thereby extending known work on the action of composition operators on model spaces. Finally, we use the equivalences between Toeplitz kernels to derive the explicit maximal vectors for several Toeplitz kernels, with symbols expressed in terms of composition operators and inner functions.