Montel,s Theorem
المؤلف:
Titchmarsh, E. C
المصدر:
The Theory of Functions, 2nd ed. Oxford, England: Oxford University Press
الجزء والصفحة:
...
11-12-2018
682
Montel's Theorem
Let 
be an analytic function of 
, regular in the half-strip 
defined by 
and 
. If 
is bounded in 
and tends to a limit 
as 
for a certain fixed value 
of 
between 
and 
, then 
tends to this limit 
on every line 
in 
, and 
uniformly for 
.
REFERENCES:
Krantz, S. G. "Montel's Theorem, First Version and Montel's Theorem, Second Version." §8.4.3 and 8.4.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 114, 1999.
Titchmarsh, E. C. The Theory of Functions, 2nd ed. Oxford, England: Oxford University Press, p. 170, 1960.
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