Аннотация:
There are many equivalent conditions for Bloch functions on the unit disc $\mathbb U = \{ \zeta \in \mathbb C \mid |\zeta|<1 \}$ The concept of a Bloch function has been extended to various complex domains in finite or infinite dimensions. In particular, a definition of a complex-valued Bloch function on a bounded homogeneous domain was given by R. Timoney, who has shown that several equivalent conditions for complex-valued Bloch functions on the complex unit disc $\mathbb U$ can be extended to finite dimensional bounded homogeneous domains.
In this talk, we begin by defining a Bloch function on a possibly infinite dimensional bounded symmetric domain and extend further to this setting several equivalent conditions for Bloch functions given by R. Timoney for finite dimensional domains.