Geodesic
A Joint Spectral Mapping Theorem for Sets of Semigroup Generators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 62-70

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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.
Keywords: multiparameter semigroup of operators, multidimensional functional calculus, Taylor spectrum, Bernstein function, spectral mapping theorem. 
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     author = {A. R. Mirotin},
     title = {A {Joint} {Spectral} {Mapping} {Theorem} for {Sets} of {Semigroup} {Generators}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a3/}
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A. R. Mirotin. A Joint Spectral Mapping Theorem for Sets of Semigroup Generators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 62-70. http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a3/