The Fourier transform of an unbounded spectral distribution
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- by Brian Kritt
- Proc. Amer. Math. Soc. 35 (1972), 74-80
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296731-X
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Abstract:
The Fourier transform of an unbounded spectral distribution is studied: An explicit integral representation is obtained; connections are drawn to the associated generalized scalar operator. It is proved that every generalized pseudo-hermitian operator is the infinitesimal generator of a temperate ${C_0}$ group.References
- N. Dunford and J. T. Schwartz, Linear operators. I: General theory, 2nd ed., Interscience, New York, 1964.
L. Hörmander, Linear partial differential operators, Die Grundlehren der math, Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
- John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028
- B. Kritt, Spectral decomposition of positive and positive-definite distributions of operators, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 865–870. MR 241972
- Brian Kritt, Generalized pseudo-hermitian operators, Proc. Amer. Math. Soc. 30 (1971), 343–348. MR 281046, DOI 10.1090/S0002-9939-1971-0281046-5
- Brian Kritt, A theory of unbounded generalized scalar operators, Proc. Amer. Math. Soc. 32 (1972), 484–490. MR 293437, DOI 10.1090/S0002-9939-1972-0293437-8
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 74-80
- MSC: Primary 47B40
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296731-X
- MathSciNet review: 0296731