About entire functions with specialL 2-properties on one-dimensional subspaces of ℂ n

The behaviour on the rays of functions from the Bergman and Fock spaces

“…in [7] the authors considered the behaviour of functions from the several-dimensional Fock spaces as restricted to the complex one-dimensional subspaces of C n . It holds F s ⊂ F u for s < u.…”

The Fejer-Riesz type result for some weighted Hilbert spaces of analytic functions in the unit disc

“…[1,2,[6][7][8]. Given a function f holomorphic in U , f (z) = ∞ n=0 a n z n , z ∈ U , one can prove by integrating in polar coordinates and using the formula Moreover, for f (z) = ∞ n=0 a n z n holomorphic in U we have…”