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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Schauder bases in the Banach spaces $ C\sp{k}({\bf T}\sp{q})$


Author: Steven Schonefeld
Journal: Trans. Amer. Math. Soc. 165 (1972), 309-318
MSC: Primary 46B15
MathSciNet review: 0293375
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0293375-5
PII: S 0002-9947(1972)0293375-5
Keywords: Schauder basis, interpolating basis, Banach space of differentiable functions
Article copyright: © Copyright 1972 American Mathematical Society