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Analyticity and parabolicity

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1701)

Summary

In Section 4.1, we characterize, in terms of the estimates of , those (ACP n ) whose propagators can be extended analytically to the sector Σ θ (for a fixed ) satisfying appropriate conditions there; such behavior of (ACP n ) is called analytic wellposedness (in Σ θ ), which will be made precise in Definition 1.2. We also treat perturbation problems about analytic wellposedness in this section. A new type of perturbation operators is introduced, besides that given in Section 2.4.

Keywords

  • Linear Operator
  • Cauchy Problem
  • Differential Operator
  • Entire Function
  • Entire Solution

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© 1998 Springer-Verlag Berlin Heidelberg

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Xiao, TJ., Liang, J. (1998). Analyticity and parabolicity. In: The Cauchy Problem for Higher Order Abstract Differential Equations. Lecture Notes in Mathematics, vol 1701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49479-9_4

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  • DOI: https://doi.org/10.1007/978-3-540-49479-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65238-0

  • Online ISBN: 978-3-540-49479-9

  • eBook Packages: Springer Book Archive