Geodesic
Averaged Wave Operators on Singular Spectrum
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 24-36

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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.
Keywords: wave operator, summation methods, singular measure
Mots-clés : Hilbert transform. 
@article{FAA_2012_46_2_a3,
     author = {V. V. Kapustin},
     title = {Averaged {Wave} {Operators} on {Singular} {Spectrum}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {24--36},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a3/}
}
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V. V. Kapustin. Averaged Wave Operators on Singular Spectrum. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 24-36. http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a3/