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Keywords:
holomorphic semigroup; Bernstein function
holomorphic semigroup; Bernstein function
Summary:
If $(e^{-tA})_{t>0}$ is a strongly continuous and contractive semigroup on a complex Banach space $B$, then $-(-A)^\alpha $, $0<\alpha <1$, generates a holomorphic semigroup on $B$. This was proved by K. Yosida in [7]. Using similar techniques, we present a class $H$ of Bernstein functions such that for all $f\in H$, the operator $-f(-A)$ generates a holomorphic semigroup.
References:
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[4] Jacob N., Schilling R.L.: Subordination in the sense of S. Bochner: An approach through pseudo differential operators. Math. Nachr. 178 (1996), 199-231. MR 1380710 | Zbl 0923.47023
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[7] Yosida K.: Functional Analysis, second edition. Springer Verlag, Berlin-Heidelberg-New York, 1968. MR 0239384
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