Displaying similar documents to “A family of Kučera spaces”

Modulation space estimates for Schrödinger type equations with time-dependent potentials

Wei Wei (2014)

Czechoslovak Mathematical Journal

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We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian ( - Δ ) κ / 2 with 1 ≤ κ ≤ 2 . Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for...

Retractions onto the Space of Continuous Divergence-free Vector Fields

Philippe Bouafia (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of m -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset X ⊆ ℝ n satisfying a mild geometric condition, there is no uniformly continuous representation operator for m -charges in X .