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Semigroup Forum

, Volume 98, Issue 3, pp 645–668 | Cite as

Modulation type spaces for generators of polynomially bounded groups and Schrödinger equations

  • Peer Christian KunstmannEmail author
Research Article
  • 72 Downloads

Abstract

We introduce modulation type spaces associated with the generators of polynomially bounded groups. Besides strongly continuous groups we study in detail the case of bi-continuous groups, e.g. weak\(^*\)-continuous groups in dual spaces. It turns out that this gives new insight in situations where generators are not densely defined. Classical modulation spaces are covered as a special case but the abstract formulation gives more flexibility. We illustrate this with an application to a nonlinear Schrödinger equation.

Keywords

Polynomially bounded groups Functional calculus Spaces associated with operators Modulation spaces 

Notes

References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for AnalysisKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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