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Schrödinger Equations in Modulation Spaces

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Studies in Phase Space Analysis with Applications to PDEs

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 84))

Abstract

We consider the linear propagator for Schrödinger equations with variable coefficients in \({\mathbb{R}}^{d}\). We show that it is bounded on some spaces arising in time–frequency analysis, known as modulation spaces. This generalizes recent results where the case of constant coefficients was considered.

2010 Mathematics Subject Classification: 35S30, 47G30, 42C15.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, I-10123, Torino, Italy

    Elena Cordero & Luigi Rodino

  2. Dipartimento di Scienze Matematiche, Politecnico di Torino, corso Duca degli Abruzzi 24, I-10129, Torino, Italy

    Fabio Nicola

Authors
  1. Elena Cordero
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  2. Fabio Nicola
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  3. Luigi Rodino
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Corresponding author

Correspondence to Elena Cordero .

Editor information

Editors and Affiliations

  1. , Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, Bologna, I-40126, Italy

    Massimo Cicognani

  2. , Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, Pisa, I-56127, Italy

    Ferruccio Colombini

  3. , Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Valerio, 12/1 12/1, Trieste, I-34127, Italy

    Daniele Del Santo

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Cordero, E., Nicola, F., Rodino, L. (2013). Schrödinger Equations in Modulation Spaces. In: Cicognani, M., Colombini, F., Del Santo, D. (eds) Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications, vol 84. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6348-1_5

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