# Radial boundary value

The value of a function , defined on the unit disc , at a boundary point , equal to the limit

of the function on the set of points of the radius leading to the point . The term "radial boundary value" is sometimes used in a generalized sense for functions given on arbitrary (including multi-dimensional) domains , where is taken to be the set of points of a normal (or its analogue) to the boundary of leading to the boundary point. For example, in the case of a bi-disc

as the radial boundary value at one takes the limit

#### References

[1] | A.I. Markushevich, "Theory of functions of a complex variable" , 1 , Chelsea (1977) (Translated from Russian) |

[2] | I.I. [I.I. Privalov] Priwalow, "Randeigenschaften analytischer Funktionen" , Deutsch. Verlag Wissenschaft. (1956) (Translated from Russian) |

#### Comments

The functions under consideration are usually analytic or harmonic functions. See also Boundary properties of analytic functions and its references; cf. also Angular boundary value; and Fatou theorem.

**How to Cite This Entry:**

Radial boundary value. E.D. Solomentsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Radial_boundary_value&oldid=15727