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
|||A.I. Markushevich, "Theory of functions of a complex variable" , 1 , Chelsea (1977) (Translated from Russian)|
|||I.I. [I.I. Privalov] Priwalow, "Randeigenschaften analytischer Funktionen" , Deutsch. Verlag Wissenschaft. (1956) (Translated from Russian)|
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.
Radial boundary value. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Radial_boundary_value&oldid=15727