Zero sets of functions from non-quasi-analytic classes
HTML articles powered by AMS MathViewer
- by R. B. Darst PDF
- Proc. Amer. Math. Soc. 40 (1973), 543-544 Request permission
Abstract:
Any closed subset $E$ of the real numbers $R$ is the zero set of some ${C^\infty }$-function $f$. One can also specify the order $d(s)$ of the zero of $f$ at each element $s$ of the set $S$ of isolated points of $E$. The present note improves this result by showing that each non-quasi-analytic class $C\{ {M_n}\}$ contains such functions.References
- Robert B. Hughes, Zero sets of functions from non-quasi-analytic classes, Proc. Amer. Math. Soc. 27 (1971), 539–542. MR 272965, DOI 10.1090/S0002-9939-1971-0272965-4
- 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 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 543-544
- MSC: Primary 26A93
- DOI: https://doi.org/10.1090/S0002-9939-1973-0323978-7
- MathSciNet review: 0323978