Associated weights for spaces of p-integrable entire functions

[EN] In analogy to the notion of associated weights for weighted spaces of analytic functions with sup-norms, p-associated weights are introduced for spaces of entire p-integrable functions, 1 <= p < infinity. As an application, necessary conditions for the boundedness of composition operators acting between general Fock type spaces are provedThe research of Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain).Bonet Solves, JA.; Mangino, EM. (2020). Associated weights for spaces of p-integrable entire functions. Quaestiones Mathematicae. 43(5/6):747-760. https://doi.org/10.2989/16073606.2019.1605420S747760435/

Composition operators on Hilbert spaces of entire functions with analytic symbols

Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is proved that if such an operator is bounded, then its symbol is a polynomial of degree at most 1, i.e., it is an affine mapping. Fock's type model for composition operators with linear symbols is established. As a consequence, explicit formulas for their polar decomposition, Aluthge transform and powers with positive real exponents are provided. The theorem of Carswell, MacCluer and Schuster is generalized to the case of Segal-Bargmann spaces of infinite order. Some related questions are also discussed.Comment: This is a final version of our previous submissions. It consists of 48 page