# Angular boundary value

From Encyclopedia of Mathematics

*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 , .

#### References

[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) |

#### Comments

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. E.D. Solomentsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Angular_boundary_value&oldid=12519

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098