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Bergman function, Genchev transform and L²-angles, for multidimensional tubes

Hyb Wojciech — 1996

CONTENTS1. Introduction.......................................................................................................52. Basic definitions, notations and facts................................................................63. Definitions of the Genchev transform................................................................84. Basic properties of the Genchev transform......................................................115. Some properties of the weight w B ..............................................................166....

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

Wojciech Hyb — 1991

Annales Polonici Mathematici

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).

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