A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

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1. [1] W. Arendt, Gaussian estimates and interpolation of the spectrum in $L^p$, Differential Integral Equations 7 (1994), 1153-1168. Zbl0827.35081
2. [2] W. Arendt and C. J. K. Batty, Tauberian theorms and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852. Zbl0652.47022
3. [3] E. Balslev, The essential spectrum of elliptic differential operators in $L^p\left({ℝ}_n\right)$, ibid. 116 (1965), 193-217. 
4. [4] C. J. K. Batty, Asymptotic stability of Schrödinger semigroups: path integral methods, Math. Ann. 292 (1992), 457-492. Zbl0736.35025
5. [5] C. J. K. Batty and D. A. Greenfield, On the invertibility of isometric semigroup representations, Studia Math. 110 (1994), 235-250. Zbl0803.47033
6. [6] C. J. K. Batty and Vũ Quôc Phóng, Stability of strongly continuous representations of abelian semigroups, Math. Z. 209 (1992), 75-88. 
7. [7] Z. Brze/xniak and B. Szafirski, Asymptotic behaviour of $L^1$ norm of solutions to parabolic equations, Bull. Polish Acad. Sci. Math. 39 (1991), 1-10. 
8. [8] E. B. Davies, Heat Kernels and Spectral Theory, Cambridge Univ. Press, Cambridge, 1989. Zbl0699.35006
9. [9] E. B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995), 141-169. Zbl0839.35034
10. [10] E. B. Davies, Long time asymptotics of fourth order parabolic equations, J. Anal. Math., to appear. Zbl0851.35018
11. [11] R. G. Douglas, On extending commutative semigroups of operators, Bull. London Math. Soc. 1 (1969), 157-159. Zbl0187.06501
12. [12] J. Esterle, E. Strouse et F. Zouakia, Stabilité asymptotique de certains semigroupes d’opérateurs et idéaux primaires de $L^1\left({ℝ}^{+}\right)$, J. Operator Theory 28 (1992), 203-227. 
13. [13] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. Zbl0144.34903
14. [14] D. Gilbarg and J. Serrin, On isolated singularities of solutions of second order elliptic differential equations, J. Anal. Math. 4 (1955-56), 309-340. Zbl0071.09701
15. [15] J.-P. Kahane et Y. Katznelson, Sur les algèbres de restrictions des séries de Taylor absolument convergentes à un fermé du cercle, ibid. 23 (1970), 185-197. 
16. [16] Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), 313-328. Zbl0611.47005
17. [17] L. H. Loomis, The spectral characterization of a class of almost periodic functions, Ann. of Math. 72 (1960), 362-368. Zbl0094.05801
18. [18] Yu. I. Lyubich, Introduction to the Theory of Banach Representations of Groups, Birkhäuser, Basel, 1988. 
19. [19] Yu. I. Lyubich and Vũ Quôc Phóng, Asymptotic stability of linear differential equations in Banach spaces, Studia Math. 88 (1988), 37-42. Zbl0639.34050
20. [20] Yu. I. Lyubich and Vũ Quôc Phóng, A spectral criterion for the almost periodicity of one-parameter semigroups, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 47 (1987), 36-41 (in Russian). 
21. [21] Yu. I. Lyubich and Vũ Quôc Phóng, A spectral criterion for asymptotic almost periodicity of uniformly continuous representations of abelian semigroups, ibid. 50 (1988), 38-43 (in Russian); English transl.: J. Soviet Math. 49 (1990), 1263-1266. 
22. [22] Z. M. Ma and M. Röckner, An Introduction to the Theory of Non-Symmetric Dirichlet Forms, Springer, Berlin, 1992. Zbl0826.31001
23. [23] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. Zbl0111.09302
24. [24] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, Berlin, 1986. Zbl0585.47030
25. [25] J. van Neerven, The Asymptotic Behaviour of a Semigroup of Linear Operators, Birkhäuser, Basel, 1996. Zbl0905.47001
26. [26] E. M. Ouhabaz, $L^{\infty }$-contractivity of semigroups generated by sectorial forms, J. London Math. Soc. 46 (1992), 529-542. Zbl0788.47034
27. [27] R. Hempel and J. Voigt, The spectrum of a Schrödinger operator in $L_p\left({ℝ}^{\nu }\right)$ is p-independent, Comm. Math. Phys. 104 (1986), 243-250. Zbl0593.35033
28. [28] G. K. Pedersen, C*-Algebras and their Automorphism Groups, Academic Press, London, 1979. Zbl0416.46043
29. [29] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer, Berlin, 1984. Zbl0549.35002
30. [30] D. W. Robinson, Elliptic Operators and Lie Groups, Oxford Univ. Press, Oxford, 1991. Zbl0747.47030
31. [31] W. Rudin, Fourier Analysis on Groups, Wiley, New York, 1992. 
32. [32] R. Rudnicki, Asymptotic stability in $L^1$ of parabolic equations, J. Differential Equations 102 (1993), 391-401. Zbl0815.35034
33. [33] M. Schechter, Spectra of Partial Differential Operators, North-Holland, Amsterdam, 1971. Zbl0225.35001
34. [34] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526. Zbl0524.35002
35. [35] Vũ Quôc Phóng, Theorems of Katznelson-Tzafriri type for semigroups of operators, J. Funct. Anal. 103 (1992), 74-84. Zbl0770.47017
36. [36] Vũ Quôc Phóng, On the spectrum, complete trajectories, and asymptotic stability of linear semi-dynamical systems, J. Differential Equations 105 (1993), 30-45. 
37. [37] Vũ Quôc Phóng, Stability and almost periodicity of trajectories of periodic processes, ibid. 115 (1995), 402-415. 

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