Continuous families of vectors that are orbits of a unitary group |
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| Authors: | Ralph deLaubenfels |
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| Institution: | Ohio State University, Department of Mathematics, Columbus, OH 43210, USA |
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| Abstract: | We characterize functions u from the real line into a Hilbert space that are the orbits of a unitary group {U(t)}t∈R; that is, u(t)=U(t)u(0), for all real t. One of the characterizations is that u be the Fourier transform of a certain type of vector-valued measure Z; we then use our characterizations to construct Z from u. |
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| Keywords: | Groups of operators Self-adjoint operators Vector-valued measures Stationary processes Time series |
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