Vol. 35, No. 3, 1970

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On the ideal structure of some algebras of analytic functions

John Eric Gilbert

Vol. 35 (1970), No. 3, 625–634

Using the Beurling-Lax description of invariant subspaces of H2(R), we describe the ideal structure of two large classes of convolution algebras whose Fourier-Laplace Transforms are entire functions. A closed ideal will be characlerized by its cospectrum or by its cospectrum together with a nonnegative number related to the “rate of decrease at infinity”; in the latter case, the closed ideals having the same cospectrum form a totally ordered family {Iξ}[0,), with Iξ Iη whenever ξ < η. New examples of algebras to which the results apply are given.

Mathematical Subject Classification
Primary: 30A98
Received: 30 September 1969
Revised: 25 April 1970
Published: 1 December 1970
John Eric Gilbert