![the results of Bass [2] may be applied because the pre-Hilbert M (x) is a subspace of the Marcinkiewicz space M of sequences in the previous section. To see this, suppose zÎM(x), then](https://images.tandf.co.uk/common/jackets/crclarge/978042922/9780429223976.jpg "the results of Bass [2] may be applied because the pre-Hilbert M (x) is a subspace of the Marcinkiewicz space M of sequences in the previous section. To see this, suppose zÎM(x), then")
ABSTRACT
J : HN (x) H(x) that preserves inner products and the respective topologies are those induced ( . , . ) N a n d ( . , . ) L 2 .
= VSnx.
Since J is an isometry, V = J-1Ux J is unitary and is given by SN, showing that the N-shift is unitary. |
Having established the Hilbert space isomorphism between HN (X) and the Hilbert space H (x) of a CS(N) random sequence, we can use any of the representations for CS random sequences to produce a corresponding representation for regular CS numerical sequences.
