Schauder bases in the Banach spaces 𝐶^{𝑘}(𝑇^{𝑞})

Schonefeld, Steven

doi:10.1090/S0002-9947-1972-0293375-5

Schauder bases in the Banach spaces $C^{k}(\textbf {T}^{q})$
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by Steven Schonefeld

Trans. Amer. Math. Soc. 165 (1972), 309-318

DOI: https://doi.org/10.1090/S0002-9947-1972-0293375-5

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Abstract:

A Schauder basis is constructed for the space ${C^k}({T^q})$ of k-times continuously differentiable functions on ${T^q}$, the product of q copies of the one-dimensional torus. This basis has the property that is also a basis for the spaces ${C^1}({T^q}),{C^2}({T^q}), \ldots ,{C^{k - 1}}({T^q})$, and an interpolating basis for $C({T^q})$.

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