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

Wojciech Hyb

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 157-161
  • ISSN: 0066-2216

Abstract

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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).

How to cite

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Wojciech Hyb. "On the spectral properties of translation operators in one-dimensional tubes." Annales Polonici Mathematici 55.1 (1991): 157-161. <http://eudml.org/doc/262277>.

@article{WojciechHyb1991,
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).},
author = {Wojciech Hyb},
journal = {Annales Polonici Mathematici},
keywords = {spectral properties of some group of unitary operators; Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube; Genchev transform; projection-valued measure},
language = {eng},
number = {1},
pages = {157-161},
title = {On the spectral properties of translation operators in one-dimensional tubes},
url = {http://eudml.org/doc/262277},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Wojciech Hyb
TI - On the spectral properties of translation operators in one-dimensional tubes
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 157
EP - 161
AB - 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).
LA - eng
KW - spectral properties of some group of unitary operators; Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube; Genchev transform; projection-valued measure
UR - http://eudml.org/doc/262277
ER -

References

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  1. [1] N. Dunford and J. T. Schwartz, Linear Operators, Vol. 2, Interscience Publishers, New York 1963. Zbl0128.34803
  2. [2] T. G. Genchev, Integral representations for functions holomorphic in tube domain, C. R. Acad. Bulgar. Sci. 37 (1984), 717-720. Zbl0576.32005
  3. [3] H. Helson, The Spectral Theorem, Lecture Notes in Math. 1227, Springer, Berlin 1986. Zbl0615.47021
  4. [4] E. Hille, Analytic Function Theory, Vol. 2, Ginn, Boston 1962. Zbl0102.29401
  5. [5] M. Skwarczyński, Alternating projections between a strip and a halfplane, Math. Proc. Cambridge Philos. Soc. 102 (1987), 121-129. Zbl0625.30012
  6. [6] E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971. Zbl0232.42007

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