A joint spectral mapping theorem for sets of semigroup generators
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In the context of the multidimensional functional calculus of semigroup generators, which is based on the class of Bernstein functions in several variables (and is also known as Bochner-Phillips multidimensional functional calculus), a spectral mapping theorem for the Taylor spectrum of a set of commuting generators is proved.
Key wordsmultiparameter semigroup of operators multidimensional functional calculus Taylor spectrum Bernstein function spectral mapping theorem
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- R. Shilling, R. Song, and Z. Vondraček, Bernstein Functions. Theory and Applications, de Greyter, Berlin-New York, 2010.Google Scholar
- W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2, Wiley, New York-London-Sidney, 1971.Google Scholar
- Ch. Berg, J. P. R. Christensen, and P. Ressel, Harmonic Analysis on Semigroups, Graduate Texts in Math., vol. 100, Springer-Verlag, New York-Berlin, 1984.Google Scholar
- A. R. Mirotin, “On multidimensional Bochner-Phillips functional calculus,” Prob. Fiz. Mat. Tekh., 1:1 (2009), 63–66.Google Scholar
- O. Bratelli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer-Verlag, New York, 1979.Google Scholar
- A. Ya. Khelemskii, Homology in Banach and Topological Algebras [in Russian], Izd. Mosk. Gos. Univ., Moscow, 1986.Google Scholar