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


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.


Polynomially bounded groups Functional calculus Spaces associated with operators Modulation spaces 



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© 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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