Translation and dilation invariant subspaces of L2 (R)

What is it about?

The closed subspaces of the Hilbert space L 2(R) which are invariant under multiplication by H^\infty(R) functions and the dilation operators f(x)\to f(sx), 1 < s, are determined as the two parameter family of subspaces L 2[a,b], which are reducing for multiplication operators, together with a four parameter family of non-reducing subspaces. The lattice and topological structure are determined and using operator algebra methods the corresponding family of orthogonal projections, with the weak operator topology, is identified as a compact connected 4-manifold.

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