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Silverman-Toeplitz theorem∗
rspuzio†
2013-03-21 18:22:28
Let {amn } be a double sequence of complex numbers and let B be a positive
real number such that:
P∞
1.
n=0 |amn | ≤ B for all m = 0, 1, 2, . . .
P∞
2. limm→∞ n=0 amn = 1
3. For every n = 0, 1, 2, . . ., it is the case that limm→∞ amn = 0
P∞
Then, if the sequence {zn } converges, the series n=0 amn zn converges and
lim zn = lim
n→∞
m→∞
∞
X
amn zn
n=0
∗ hSilvermanToeplitzTheoremi created: h2013-03-21i by: hrspuzioi version: h36531i Privacy setting: h1i hTheoremi h40B05i
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