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

• Autorzy: Wojciech Hyb
• Języki publikacji: EN

Abstrakty

EN

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).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 55
• Numer: 1
• Strony: 157-161

Daty

wydano

1991

otrzymano

1990-09-14

Twórcy

autor

Wojciech Hyb

• Department of Applied Mathematics, Agricultural Academy, Nowoursynowska 166, 02-766 Warszawa, Poland

Bibliografia

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