Translation invariants for periodic Denjoy-Carleman classes
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- by P. X. Gallagher PDF
- Proc. Amer. Math. Soc. 120 (1994), 139-141 Request permission
Abstract:
The Denjoy-Carleman classes in real ${C^\infty }(\mathbb {R}/\mathbb {Z})$ on which the derivative sequence ${f^{(n)}}(x)$ at any point is a complete set of invariants are exactly the ones on which the integrals of products of derivatives ${f^{({n_1})}} \cdots {f^{({n_r})}}$ are a complete set of invariants up to translation.References
- Roy L. Adler and Alan G. Konheim, A note on translation invariants, Proc. Amer. Math. Soc. 13 (1962), 425–428. MR 146652, DOI 10.1090/S0002-9939-1962-0146652-1 T. Carleman, Les fonctions quasi analytiques, Gauthier-Villars, Paris, 1926. S. Mandelbrojt, Series de Fourier et classes quasi-analytiques de fonctions, Gauthier-Villars, Paris, 1935.
- S. Mandelbrojt, Some theorems connected with the theory of infinitely differentiable functions, Duke Math. J. 11 (1944), 341–349. MR 10177
- S. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952 (French). MR 0051893
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 139-141
- MSC: Primary 46E99; Secondary 26E10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1172950-X
- MathSciNet review: 1172950