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ArticleOriginal scientific text

Title

On the growth of analytic semigroups along vertical lines

Authors 1, 2

Affiliations

  1. Departamento de Matemáticas, Universidad de Zaragoza, E-50009 Zaragoza, Spain
  2. Département de mathématiques et de statistique, Université Laval, Québec, Canada G1K 7P4

Abstract

We construct two Banach algebras, one which contains analytic semigroups (az)Rez>0 such that |a1+iy|→∞ arbitrarily slowly as |y|→∞, the other which contains ones such that |a1+iy|→∞ arbitrarily fast

Bibliography

  1. [BH] A. Beurling and H. Helson, Fourier-Stieltjes transforms with bounded powers, Math. Scand. 1 (1953), 120-126.
  2. [C] T. Carleman, Sur un théorème de Weierstrass, Ark. Mat. Astronom. Fys. 20B (1927), 1-5.
  3. [E1] J. Esterle, A complex-variable proof of the Wiener Tauberian theorem, Ann. Inst. Fourier (Grenoble) 30 (1980), 91-96.
  4. [E2] J. Esterle, Rates of decrease of sequences of powers in commutative radical Banach algebras, Pacific J. Math. 94 (1981), 61-82.
  5. [E3] J. Esterle, Elements for a classification of commutative radical Banach algebras, in: Proc. Conf. on Radical Banach Algebras and Automatic Continuity (Long Beach, 1981), J. M. Bachar and others (ed.), Lecture Notes in Math. 975, Springer, Berlin, 1983, 4-65.
  6. [E4] J. Esterle, private communication.
  7. [EG] J. Esterle and J. E. Galé, Regularity of Banach algebras generated by analytic semigroups satisfying some growth conditions, Proc. Amer. Math. Soc. 92 (1984), 377-380.
  8. [G] J. E. Galé, Banach algebras generated by analytic semigroups having compactness properties on vertical lines, in: Proc. Conf. on Automatic Continuity and Banach Algebras (Canberra, 1989), R. J. Loy (ed.), Proc. Centre Math. Anal. Austral. Nat. Univ. 21, Austral. Nat. Univ., Canberra, 1989, 126-143.
  9. [GW] J. E. Galé and M. C. White, An analytic semigroup version of the Beurling-Helson theorem, Math. Z. 225 (1997), 151-165.
  10. [GM] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York, 1979.
  11. [K] J.-P. Kahane, Séries de Fourier absolument convergentes, Springer, Berlin, 1970.
  12. [R] T. J. Ransford, Norm inequalities for holomorphic semigroups, Israel J. Math. 97 (1997), 157-173.
  13. [S] A. M. Sinclair, Continuous Semigroups in Banach Algebras, Cambridge Univ. Press, Cambridge, 1982.
  14. [W] M. C. White, Strong Wedderburn decompositions of Banach algebras containing analytic semigroups, J. London Math. Soc. (2) 49 (1994), 331-342.
Studia Mathematica
2000/138/2
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Pages:
165-177
Main language of publication
English
Received
1999-01-12
Accepted
1999-11-15
Published
2000
Exact and natural sciences