The Moment Problem by Konrad Schmüdgen

Author:Konrad Schmüdgen
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(12.8)

Example 12.4

Let us assume that the set f is of the form

If g: = {g 1, …, g l } and denotes the ideal of generated by h 1, …, h m , then

(12.9)

We prove (12.9). The first equality of (12.9) and the inclusions and are clear from the corresponding definitions. The identity

implies that . Hence and ∘

Another important concept is introduced in the following definition.

Definition 12.5

Let Q be a quadratic module or a semiring of A. Define

We shall say that Q is Archimedean if A b (Q) = A, or equivalently, for every a ∈ A there exists a λ > 0 such that λ − a ∈ A.

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