Quasi-analyticity criteria of Salinas - Korenblum type for general domains

Abstract

We prove a criterion of quasi-analyticity in a boundary point of a rather general domain (not necessarily convex and simply-connected) if in a vicinity of this point the domain is close in some sense to an angle or is comparable with it.

Regularization of sequences in sense of E. M. Dyn'kin

“…ℎ( ) +1 = ′ < ∞ ( 0). Now convergence of series (6) follows from Theorem 7 in work [5]. Then there exists a function = ( ), 0 < ( ) ↓ 0, ( ) ↓ 0, 2 ( ) ↑ as → ∞ such that [6] 1) 1…”

“…A sequence { } ( > 0) is called weakly regular if numbers = ! satisfy Conditions a), c) of the definition of the regular sequence [6]. Each its regular minorant (if it exists) will be called regularization in the E.M. Dyn'kin sense.…”