CONVOLUTION ROOTS OF RADIAL POSITIVE DEFINITE FUNCTIONS WITH COMPACT SUPPORT August 20, 2003

Abstract

A classical theorem of Boas, Kac, and Krein states that a characteristic function φ with φ(x) = 0 for |x| ≥ τ admits a representation of the form φ(x) = ∫ u(y)u(y + x) dy, x ∈ R where the convolution root u ∈ L2(R) is complex-valued with u(x) = 0 for |x| ≥ τ/2. The result can be expressed equivalently as a factorization theorem for entire functions of… (More)

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