Singularity
of an analytic function
A set of singular points (cf. Singular point) of an analytic function in the complex variables
,
, defined by some supplementary conditions. In particular, isolated singular points (cf. Isolated singular point) are sometimes called isolated singularities.
A set such that in a domain
adjoining
there is defined a single-valued analytic function
for which the question arises of the possibility of analytic continuation of
to
. For example, let
be a domain of the space
, let
be a compactum contained in
, and let
be holomorphic on
.
is then a possible singularity of
, and the question of analytic continuation (perhaps under certain supplementary conditions) of
onto the entire domain
arises; in other words, the question of "elimination" or "removal" of the singularity
.
See also Removable set.
Comments
For references see also Singular point of an analytic function and Extension theorems (in analytic geometry). See also Hartogs theorem.
Singularity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Singularity&oldid=18225