fundamental sequence


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fundamental sequence

[¦fən·də¦ment·əl ′sē·kwəns]
(mathematics)
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k]) [member of] w(gI), is said to be modal fundamental sequence if for every [epsilon] > 0 there exists [k.
i)]} be any fundamental sequence in the space h(gI), where {[[?
k]} is a fundamental sequence in gI for every fixed k [member of] N.
i)]} is an arbitrary fundamental sequence, the space h(gI) is complete.
i)]} be any fundamental sequence in the space [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The case of Frechet-Schwartz spaces follows analogously if, instead of a fundamental sequence of bounded sets, we take a fundamental sequence of zero neighbourhoods.
n]) is a fundamental sequence of bounded sets (here [GAMMA] stands for the absolutely convex hull).
For their duals the proof is the same if, instead of a fundamental sequence of zero neighbourhoods, we take a fundamental sequence of bounded sets.
The polynomials also may be defined by an orthogonal ization procedure, if it is applied to the fundamental sequence {[x.
In particular, the algorithm of inverse orthogonalization of the fundamental sequence results in redistribution of the zeros.

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