Averaged wave operators on singular spectrum
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- Kapustin, V.V. Funct Anal Its Appl (2012) 46: 100. doi:10.1007/s10688-012-0016-2
We prove the existence of pairs of unitary (or self-adjoint) operators with singular spectral measure whose difference is a rank-two operator for which the Abel wave operators fail to exist. Also, we discuss the closely related problem of constructing the Hilbert transform with respect to a singular measure on the unit circle.
Key wordswave operator summation methods singular measure Hilbert transform
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