Namespaces
Variants
Actions

Non-singular boundary point

From Encyclopedia of Mathematics
Revision as of 17:02, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

regular boundary point

An accessible boundary point (cf. Attainable boundary point) of the domain of definition of a single-valued analytic function of a complex variable such that has an analytic continuation to along any path inside to . In other words, a non-singular boundary point is accessible, but not singular. See also Singular point of an analytic function.


Comments

Note that the same point in the boundary of may give rise to several different accessible boundary points, some of which may be singular, others regular. E.g., consider the domain , and the function , where is the principal value of . Then "above" there are two accessible boundary points: one singular, corresponding to approach along , ; one regular, corresponding to approach along , .

References

[a1] A.I. Markushevich, "Theory of functions of a complex variable" , 3 , Chelsea (1977) pp. Chapts. 2; 8 (Translated from Russian)
How to Cite This Entry:
Non-singular boundary point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-singular_boundary_point&oldid=13119
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article