On Cantor's functionals (Q2837287)
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scientific article; zbMATH DE number 6186445
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Cantor's functionals |
scientific article; zbMATH DE number 6186445 |
Statements
10 July 2013
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Cantor functional
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uniqueness of functional series
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Pringsheim convergence
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double series representation
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0.9077616
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0.8954236
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On Cantor's functionals (English)
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The author introduces the idea of systems of functions having the ``Cantor property'', i.e. \(\sum^\infty_{i=0} a_i\varphi_i(x)\) converges to zero on some set \(A\subset[0, 1]\) then all \(a_i\) are zero. Constructing now a linear space of functions which can be represented with the help of a system having the Cantor property and defining corresponding functionals, the main result states that coefficients of functions admitting a double series representation can be calculated with the help of these functionals.
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