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

Annales Polonici Mathematici (1991)

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

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topWojciech 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

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

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