On the nonexistence of a projection from functions of $x$ to functions of $x^{n}$
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- by P. Milman PDF
- Proc. Amer. Math. Soc. 63 (1977), 87-90 Request permission
Abstract:
The subspace ${\phi ^ \ast }{C^\infty }({{\mathbf {R}}^1}) \subset {C^\infty }({{\mathbf {R}}^1})$ of all ${C^\infty }$ functions of $\phi (x) = {x^n},n = 1,2,3, \ldots$, is a closed subspace of ${C^\infty }({{\mathbf {R}}^1})$ by Glaeserâs Composition Theorem. We prove that for $n > 2$ there does not exist a linear continuous projection $\pi$ from ${C^\infty }({{\mathbf {R}}^1})$ onto ${\phi ^ \ast }{C^\infty }({{\mathbf {R}}^1})$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 87-90
- MSC: Primary 58D15; Secondary 26A93
- DOI: https://doi.org/10.1090/S0002-9939-1977-0440600-3
- MathSciNet review: 0440600