Abstract:
The problem of spectral synthesis for a subspace W invariant with respect to a differential operator with constant coefficients was reduced earlier to verification that its annihilator submodule I=AnW is ample. In the present article the property of ampleness is split into two parts – stability, and the property of being saturated. The latter properties are subjected to a systematic investigation.
Citation:
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. II. The module method”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 1–15
A. B. Shishkin, “Spectral synthesis for systems of differential operators with
constant coefficients”, Sb. Math., 194:12 (2003), 1865–1898
I. F. Krasichkov-Ternovskii, A. B. Shishkin, “Local description of closed submodules of a special module of entire functions of exponential type”, Sb. Math., 192:11 (2001), 1621–1638
I. F. Krasichkov-Ternovskii, “Spectral synthesis and local description for several variables”, Izv. Math., 63:4 (1999), 729–755
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. III: Ample submodules”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 165–188
I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. IV: Synthesis”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 407–426
Citation in format AMSBIB
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