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Radial Limits of Bloch Functions in the unit Disc
Author(s) -
Ullrich David C.
Publication year - 1986
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/18.4.374
Subject(s) - mathematics , mathematical analysis , limit (mathematics) , bounded function , boundary (topology) , bloch wave , unit interval , pure mathematics , physics , quantum mechanics
Although a function in the Bloch space may have no radial limits, it is shown that there exist bounded linear functionals which give ‘average radial limits’ over an interval on the boundary. An ‘abelian–tauberian’ theorem is proved, characterizing the existence of a radial limit at a given boundary point in terms of these functionals.