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On A Uniqueness Condition For Cr Functions On Hypersurfaces

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Author list: Daghighi, Abtin

Publication year: 2018

Start page: 68

End page: 79

Number of pages: 12

ISSN: 1821-1291

View additional information: View in Web of Science™

Abstract

Let f be a smooth CR function on a smooth hypersurface M subset of C-n, such that f vanishes to infinite order along a C-infinity-smooth curve gamma subset of M. Assume that for each q is an element of gamma there exists a truncated double cone C at q in M, such that at least one of the following three conditions holds true: (a) There is a constant theta is an element of R, such that C subset of {|Re(e(i theta)f)| <= |Im(e(i theta)f)|}. (b) C subset of {Ref >= 0}. (c) |f(z)|(|z-q|) -> 0, z -> q, z subset of C. Then f vanishes on an M-open neighborhood of gamma.

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