On the spectral properties of translation operators in one-dimensional tubes
Volume 55 / 1991
Annales Polonici Mathematici 55 (1991), 157-161
DOI: 10.4064/ap-55-1-157-161
Abstract
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).
