Zero sets of functions from non-quasi-analytic classes
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- by Robert B. Hughes PDF
- Proc. Amer. Math. Soc. 27 (1971), 539-542 Request permission
Erratum: Proc. Amer. Math. Soc. 39 (1973), 651.
Abstract:
It is well known that any closed subset of the line is the zero set of a ${C^\infty }$-function. One can also specify the orders of the zeros at the isolated points. The present paper improves this result by replacing the class of ${C^\infty }$-functions by any non-quasi-analytic class of ${C^\infty }$-functions.References
- S. Mandelbrojt, Analytic functions and classes of infinitely differentiable functions, Rice Inst. Pamphlet 29 (1942), no. 1, 142. MR 6354
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 539-542
- MSC: Primary 26.80
- DOI: https://doi.org/10.1090/S0002-9939-1971-0272965-4
- MathSciNet review: 0272965