On the Growth of the Resolvent of a Toeplitz Operator
DOI:
https://doi.org/10.15407/mag20.04.05Анотація
Досліджено зростання резольвенти оператора Тепліца $T_b$, визначеного на просторі Гарді, через відстань до його спектра $\sigma(T_b)$. Нас в першу чергу цікавить випадок, коли символ $b$ є поліномом Лорана, тобто відповідна матриця Тепліца $T_b$ є стрічковою. Доведено, що для довільного такого символу зростання резольвенти є квадратичним (3.1), а за деяких додаткових припущень - лінійним (2.1). Доведено також квадратичне зростання резольвенти для певного класу нераціональних символів.
Mathematical Subject Classification 2020: 47B35, 30H10, 47G10
Ключові слова:
оператор Теплiца, простiр Гардi, зростання резольвенти, полiном Лорана з властивiстю Жордана, регулярнi полiноми ЛоранаПосилання
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