On the growth of analytic semigroups along vertical lines

José Galé; Thomas Ransford

Studia Mathematica (2000)

  • Volume: 138, Issue: 2, page 165-177
  • ISSN: 0039-3223

Abstract

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We construct two Banach algebras, one which contains analytic semigroups ( a z ) R e z > 0 such that | a 1 + i y | → ∞ arbitrarily slowly as | y | → ∞ , the other which contains ones such that | a 1 + i y | → ∞ arbitrarily fast

How to cite

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Galé, José, and Ransford, Thomas. "On the growth of analytic semigroups along vertical lines." Studia Mathematica 138.2 (2000): 165-177. <http://eudml.org/doc/216696>.

@article{Galé2000,
abstract = {We construct two Banach algebras, one which contains analytic semigroups $(a^z)_\{Re z>0\}$ such that $|a^\{1+iy\}| → ∞$ arbitrarily slowly as $|y| → ∞$, the other which contains ones such that $|a^\{1+iy\}| → ∞$ arbitrarily fast},
author = {Galé, José, Ransford, Thomas},
journal = {Studia Mathematica},
keywords = {analytic semigroups},
language = {eng},
number = {2},
pages = {165-177},
title = {On the growth of analytic semigroups along vertical lines},
url = {http://eudml.org/doc/216696},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Galé, José
AU - Ransford, Thomas
TI - On the growth of analytic semigroups along vertical lines
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 2
SP - 165
EP - 177
AB - We construct two Banach algebras, one which contains analytic semigroups $(a^z)_{Re z>0}$ such that $|a^{1+iy}| → ∞$ arbitrarily slowly as $|y| → ∞$, the other which contains ones such that $|a^{1+iy}| → ∞$ arbitrarily fast
LA - eng
KW - analytic semigroups
UR - http://eudml.org/doc/216696
ER -

References

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  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. Zbl0708.46048
  9. [GW] J. E. Galé and M. C. White, An analytic semigroup version of the Beurling-Helson theorem, Math. Z. 225 (1997), 151-165. Zbl0874.46031
  10. [GM] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York, 1979. Zbl0439.43001
  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. Zbl0899.47027
  13. [S] A. M. Sinclair, Continuous Semigroups in Banach Algebras, Cambridge Univ. Press, Cambridge, 1982. Zbl0493.46042
  14. [W] M. C. White, Strong Wedderburn decompositions of Banach algebras containing analytic semigroups, J. London Math. Soc. (2) 49 (1994), 331-342. Zbl0833.46047

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