We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).
@article{bwmeta1.element.bwnjournal-article-apmv55z1p157bwm,
author = {Wojciech Hyb},
title = {On the spectral properties of translation operators in one-dimensional tubes},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {157-161},
zbl = {0766.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p157bwm}
}
Wojciech Hyb. On the spectral properties of translation operators in one-dimensional tubes. Annales Polonici Mathematici, Tome 55 (1991) pp. 157-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p157bwm/
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