Silverman-Toeplitz theorem

Let {amn} be a double sequence of complex numbersMathworldPlanetmathPlanetmath and let B be a positive real number such that:

  1. 1.

    n=0|amn|B for all m=0,1,2,

  2. 2.


  3. 3.

    For every n=0,1,2,, it is the case that limmamn=0

Then, if the sequencePlanetmathPlanetmath {zn} converges, the series n=0amnzn converges and

Title Silverman-Toeplitz theorem
Canonical name SilvermanToeplitzTheorem
Date of creation 2013-03-22 14:51:28
Last modified on 2013-03-22 14:51:28
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 10
Author rspuzio (6075)
Entry type Theorem
Classification msc 40B05