Angular boundary value

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boundary value along a non-tangential path

The value associated to a complex function defined in the unit disc at a boundary point , equal to the limit

of on the set of points of the angular domain

under the condition that this limit exists for all , , and hence does not depend on . The term is sometimes applied in a more general sense to functions given in an arbitrary (including a higher-dimensional) domain ; for one takes the intersection with of an angular (or conical) domain with vertex , with axis normal to the boundary at and with angle , .


[1] A.I. Markushevich, "Theory of functions of a complex variable" , 1–2 , Chelsea (1977) (Translated from Russian)
[2] I.I. [I.I. Privalov] Priwalow, "Randeigenschaften analytischer Funktionen" , Deutsch. Verlag Wissenschaft. (1956) (Translated from Russian)


An angular boundary value is also called a non-tangential boundary value. Cf. Boundary properties of analytic functions.

How to Cite This Entry:
Angular boundary value. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article