Logarithms and imaginary powers of closed linear operators

Integral Equations and Operator Theory

Volumn 38, Issue 4, 2000, Pages 458-500

  Okazawa, Noboru ^a  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039608334     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01228608     Document Type: Article

References (54)

1. H. Amann, Linear and Quasilinear Parabolic Problems, I: Abstract Linear Theory, Monographs in Math., vol. 89, Birkhäuser Verlag, Basel and Boston, 1995.
2. W. Arendt, O. El Mennaoui and M. Hieber, Boundary values of holomorphic semigroups, Proc. Amer. Math. Soc. 125 (1997), 635-647.
3. J.B. Baillon and Ph. Clément, Examples of unbounded imaginary powers of operators, J. Functional Anal. 100 (1991), 419-434.
4. 2 decay for the Navier-Stokes flow in halfspaces, Math. Ann. 282 (1988), 139-155.
5. H. Brezis, Quelques propriétés des opérateurs monotones et des semi-groupes non linéaires, Lecture Notes in Math., vol. 543, Springer-.Verlag, Berlin and New York, 1976, pp. 56-82.
6. H. Brezis, M.G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space, Comm. Pure Appl. Math. 23 (1970), 123-144.
7. A.S. Carasso and T. Kato, On subordinated holomorphic semigroups, Trans. Amer. Math. Soc. 327 (1991), 867-878.
8. R.R. Coifman and G. Weiss, Transference Method in Analysis, CBMS Regional Conference Ser. in Math. No. 31, Amer. Math. Soc., Providence, Rhode Island, 1977.
9. E.B. Davies, One-Parameter Semigroups, London Mathematical Society Monographs, vol. 15, Academic Press, London and New York, 1980.
10. p regularity for abstract differential equations, Lecture Notes in Math., vol. 1540, Springer-Verlag, Berlin and New York, 1993, pp. 25-38.
11. G. Dore and A. Venni, On the closedness of the sum of two closed operators, Math. Z. 196 (1987), 189-201.
12. H.O. Fattorini, The Cauchy Problem, Encyclopedia of Math. Appl., vol. 18, Cambridge Univ. Press (Addison-Wesley Publishing Com.), New York (London), 1984 (1983).
13. p estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Functional Anal. 102 (1991), 72-94.
14. J. Glimm and A. Jaffe, Singular perturbations of selfadjoint operators, Comm. Pure Appl. Math. 22 (1969), 401-414.
15. J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.
16. E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann. 123 (1951), 415-438.
17. M. Hieber, A. Holderrieth and F. Neubrander, Regularized semigroups and systems of linear partial differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 19 (1992), 363-379.
18. E. Hille and R.S. Phillips, Functional Analysis and Semi-groups, Colloquium Publications, vol. 31, Amer. Math. Soc., Providence, Rhode Island, 1957.
19. T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semigroups, Proc. Japan Acad. 35 (1959), 467-468.
20. T. Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan 13 (1961), 246-274.
21. T. Kato, Fractional powers of dissipative operators, II, J. Math. Soc. Japan 14 (1962), 242-248.
22. T. Kato, A generalization of the Heinz inequality, Proc. Japan Acad. 37 (1961), 305-308.
23. T. Kato, Perturbation Theory for Linear Operators, Grundlehren Math. Wiss., vol. 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976.
24. T. Kato, Perturbation Theory for Linear Operators, Grundlehren Math. Wiss., vol. 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976.
25. H. Komatsu, Fractional powers of operators, Pacific J. Math. 19 (1966), 285-346.
26. H. Komatsu, Fractional powers of operators, VI: Interpolation of non-negative operators and imbedding theorems, J. Fac. Sci. Univ. Tokyo, Sec. IA 19 (1972), 1-63.
27. S.G. Krein, Linear Differential Equations in Banach Space, Translations of Math. Mono., vol. 29, Amer. Math. Soc., Providence, Rhode Island, 1971.
28. H. Langer, Über die Wurzeln eines Maximalen Dissipativen Operatoren, Acta Math. Acad. Sci. Hungary 13 (1962), 415-424.
29. C. Le Merdy, The similarity problem for bounded analytic semigroups on Hilbert space, Semigroup Forum 56 (1998), 205-224.
30. V.A. Liskevich and M.A. Perelmuter, Analyticity of submarkovian semigroups, Proc. Amer. Math. Soc. 123 (1995), 1097-1104.
31. C. Martinez, M. Sanz and L. Marco, Fractional powers of operators, J. Math. Soc. Japan 40 (1988), 331-347.
32. A. McIntosh, Operators which have an H∞ functional calculus, Miniconference on Operator Theory and Partial Differential Equations, 1986. Proceedings of the Centre for Mathematical Analysis, vol. 14, Australian National University, Canberra, 1986, pp. 210-231.
33. A. McIntosh and A. Yagi, Operators of type ω without a bounded H∞-functional calculus, Miniconference on Operators in Analysis, 1989. Proceedings of the Centre for Mathematical Analysis, vol. 24, Australian National University, Canberra, 1990, pp. 159-172.
34. S. Monniaux, A perturbation result for bounded imaginary powers, Arch. Math. 68 (1997), 407-417.
35. S. Monniaux and J. Prüss, A theorem of the Dore-Venni type for noncommuting operators, Trans. Amer. Math. Soc. 349 (1997), 4787-4814.
36. T. Muramatu, Interpolation Spaces and Linear Operators, Kinokuniya, Tokyo, 1985.
37. V. Nollau, Über den Logarithmus abgeschlossener Operatoren in Banachschen Räumen, Acta Sci. Math. 30 (1969), 161-174.
38. N. Okazawa, Singular perturbations of m-accretive operators, J. Math. Soc. Japan 32 (1980), 19-44.
39. N. Okazawa, Sectorialness of second order elliptic operators in divergence form, Proc. Amer. Math. Soc. 113 (1991), 701-706.
40. p-theory of Schrödinger operators with strongly singular potentials, Japanese J. Math. 22 (1996), 199-239.
41. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Math. Sciences, vol. 44, Springer-Verlag, Berlin and New York, 1983.
42. J. Prüss, Evolutionary Integral Equations and Applications, Mono. in Math., vol. 87, Birkhäuser Verlag, Basel and Boston, 1993.
43. J. Prüss and H. Sohr, On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429-452.
44. p-spaces, Hiroshima Math. J. 23 (1993), 161-192.
45. B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hubert Space, North-Holland, Amsterdam, 1970.
46. H. Tanabe, Equations of Evolution, Monographs and Studies in Math., vol. 6, Pitman, London and San Francisco, 1979.
47. N. Tanaka, On the exponentially bounded C-semigroups, Tokyo J. Math. 10 (1987), 107-117.
48. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
49. A. Venni, A counterexample concerning imaginary powers of linear operators, Lecture Notes in Math., vol. 1540, Springer-Verlag, Berlin and New York, 1993, pp. 381-387.
50. A. Yagi, Applications of the purely imaginary powers of operators in Hilbert spaces, J. Functional Anal. 73 (1987), 216-231.
51. A. Yoshikawa, On the logarithm of closed linear operators, Proc. Japan Acad. 49 (1973), 169-173.
52. K. Yosida, Ergodic theorems for pseudo-resolvents, Proc. Japan Acad. 37 (1961), 422-425.
53. K. Yosida, Functional Analysis, Grundlehren Math. Wiss., vol. 123, Springer-Verlag, Berlin and New York, 1965; 6th ed., 1980.
54. K. Yosida, Functional Analysis, Grundlehren Math. Wiss., vol. 123, Springer-Verlag, Berlin and New York, 1965; 6th ed., 1980.