On the spectral properties of translation operators in one-dimensional tubes

Tom 55 / 1991

Wojciech Hyb Annales Polonici Mathematici 55 (1991), 157-161 DOI: 10.4064/ap-55-1-157-161


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).


  • Wojciech Hyb

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