Spectral mapping theorems for holomorphic functional calculi

Journal of the London Mathematical Society

Volumn 71, Issue 3, 2005, Pages 723-739

  Haase, Markus ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644620763     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/S0024610705006538     Document Type: Article

References (21)

1. D. ALBRECHT, X. DUONG and A. MCINTOSH, 'Operator theory and harmonic analysis', Instructional Workshop on Analysis and Geometry (Canberra, 1995) -Part III (Australian National University, Canberra, 1996) 77-136.
2. W. ARENDT, 'Semigroups and evolution equations: functional calculus, regularity and kernel estimates', Handbook of differential equations (ed. C. M. Dafermos and E. Feireisl, North-Holland, Amsterdam, 2004) 3-111.
3. W. ARENDT, C. J. K. BATTY, M. HIEBER and F. NEUBRANDER, Vector-valued Laplace transforms and Cauchy problems, Monographs in Mathematics 96 (Birkhäuser, Basel, 2001).
4. W. G. BADE, 'An operational calculus for operators with spectrum in a strip', Pacific J. Math. 3 (1953) 257-290.
5. A. BÁTKAI and E. FAŠANGA, 'The spectral mapping theorem for Davies' functional calculus', Rev. Roumaine Math. Pures Appl. 48 (2003) 365-372.
6. R. DELAUBENFELS, 'A holomorphic functional calculus for unbounded operators', Houston J. Math. 13 (1987) 545-548.
7. R. DELAUBENFELS, 'Unbounded holomorphic functional calculus and abstract Cauchy problems for operators with polynomially bounded resolvents', J. Funct. Anal. 114 (1993) 348-394.
8. G. DORE, 'Fractional powers of closed operators', unpublished notes, 2003.
9. N. DUNFORD and J. T. SCHWARTZ, Linear operators. I: General theory, Pure and Applied Mathematics 6 (John Wiley, 1958).
10. K.-J. ENGEL and R. NAGEL, One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics 194 (Springer, Berlin, 2000).
11. E. FAŠANGOVÁ, 'Spectral mapping theorem for the functional calculus for an operator having BIP', Ulmer Sem. Funktionalanalysis Differenzialgleichungen 8 (2003) 190-203.
12. J. E. GALÉ and T. PYTLIK, 'Functional calculus for infinitesimal generators of holomorphic semigroups', J. Funct. Anal. 150 (1997) 307-355.
13. ∞-calculus', Semigroup Forum 66 (2003) 288-304.
14. M. HAASE, 'Spectral properties of operator logarithms', Math. Z. 245 (2003) 76-79.
15. M. HAASE, The functional calculus for sectorial operators, Operator Theory: Advances and Applications (Birkhäuser, Basel, 2005).
16. M. HAASE, 'A general framework for holomorphic functional calculi', Proc. Edinburgh Math. Soc., to appear.
17. E. HILLE and R. S. PHILLIPS, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications XXXI (American Mathematical Society, Providence, RI, 1974).
18. C. MARTÍNEZ CARRACEDO and M. SANZ ALIX, The theory of fractional powers of operators (North-Holland, Amsterdam, 2001).
19. ∞ functional calculus', Miniconference on Operator Theory and Partial Differential Equations (North Ryde, 1986) (Australian National University, Canberra, 1986) 210-231.
20. F. PERIAGO and B. STRAUB, 'A functional calculus for almost sectorial operators and applications to abstract evolution equations', J. Evol. Equ. 2 (2002) 41-68.
21. 0-groups', Integral Equations Operator Theory 36 (2000) 349-369.