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A quasianalytic singular spectrum with respect to the Denjoy-Carleman class

Published online by Cambridge University Press:  22 January 2016

Soon-Yeong Chung  and
Dohan Kim
Soon-Yeong Chung
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea, [email protected]
Dohan Kim
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea, [email protected]
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Abstract

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Making use of the FBI (Fourier-Bros-Iagolnitzer) transforms we simplify the quasianalytic singular spectrum for the Fourier hyperfunctions, which was defined for distributions by Hörmander as follows; for any Fourier hyperfunction u, (x0, ξ0) does not belong to the quasianalytic singular spectrum W FM(u) if and only if there exist positive constants C, γ and N, and a neighborhood of x0 and a conic neighborhood Г of ξ0 such that

for all x ∈ U, |ξ| ∈ Γ and |ξ| ≥ N, where M(t) is the associated function of the defining sequence Mp. This result simplifies Hörmander’s definition and unify the singular spectra for the C∞ class, the analytic class and the Denjoy-Carleman class, both quasianalytic and nonquasianalytic.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 148 , December 1997 , pp. 137 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

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