Abstract
AbstractThe paper connects rather general statements about the direct sum decomposition of a Hilbert space generated by isometries with the study of analytic type subspaces in weighted $$L_2$$
L
2
-spaces over the unit disk $${\mathbb {D}}$$
D
or the complex plane $${\mathbb {C}}$$
C
, and with characterization of the so-called radial operators acting on these spaces. We characterize the properties of the so-called (m, n)-analytic functions, those that are annihilated by $$\frac{\partial ^m }{\partial z^m}\frac{\partial ^n }{\partial {{\overline{z}}}^n}$$
∂
m
∂
z
m
∂
n
∂
z
¯
n
, which as particular cases include analytic, anti-analytic, harmonic, and various related to them functions. We characterize also the so-called radial operators, with a particular attention to Toeplitz ones, that act on different subspaces of our weighted $$L_2$$
L
2
-spaces.
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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1. Extended Fock Space Formalism and Polyanalytic Functions;Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis;2022-11-04