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We utilize the concept of an abstract Wiener space to prove a converse to a theorem of Minlos, thereby obtaining necessary and sufficient conditions for a Hilbert subspace of      S ′ ( R d ) \mathcal {S}’({{\text {R}}^d})       to support a given Gaussian process over      S ( R d ) \mathcal {S}({{\text {R}}^d})      .

Support properties of Gaussian processes over Schwartz space