Abstract:
Let π1(z),…,πq(z)π1(z),…,πq(z) be a system of polynomials of the complex variable zz. In connection with the problem of spectral synthesis for systems of differential operators
π1(D),…,πq(D)π1(D),…,πq(D), D=d/dzD=d/dz, the problem of the local description of closed submodules is considered for a special module of entire functions over the ring C[π1,…,πq]. It is shown that this problem can be reduced to the local description over the ring C[l], where l is the Luroth polynomial associated with the system π1(z),…,πq(z).
Citation:
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