On the Existence of a Maximizer for the Strichartz Inequality

By Markus Kunze. 2003

71 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e52c8e1b62203f8c965fd538d38f9e52e37cf0a4

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A Sharp Inequality for the Strichartz Norm (2008, background): “ID 34080, 18 pp. [7] M. Kunze, On the existence of a maximizer for the Strichartz inequality, Comm. Math.”
Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation (2009, methodology): “Kunze [13] treated the d = 1 case and showed that maximizers exist by an elaborate concentration-compactness method; when d = 1, 2, Foschi [7] explicitly determined the best constants and showed that the only maximizers are Gaussians by using the sharp Cauchy-Schwarz inequality and the space-time Fo”
Maximizers for the Strichartz Inequality (2004, background): “This is the case that was considered in [6].”
The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality (2008, methodology): “For the problem of existence of such optimal S schr and explicitly characterizing the maximizers, Kunze [19] treated the d = 1 case and showed that maximizers exist by an elaborate concentration-compactness method.”
A refinement of the Strichartz inequality for the wave equation with applications (2012, background): “For progress on closely related problems see [3], [7], [9], [11,12], [18], [19], [20], [27], [43], [49], [53] and [54].”
Existence of maximizers for Sobolev–Strichartz inequalities (2011, background): “[10] M. Kunze, On the existence of a maximizer for the Strichartz inequality, Comm. Math.”
On sharp Strichartz inequalities in low dimensions (2006, methodology): “By using an elaborate application of the concentration compactness method, Markus Kunze showed in [5] that (1.”
Maximizers for the Strichartz Inequalities for the wave equation (2009, methodology): “[18] M. Kunze, On the existence of a maximizer for the Strichartz inequality, Comm. Math.”
Existence of Extremals for a Fourier Restriction Inequality (2010, background): “The presence of these symmetries among the extremizers for P2 implies that, in the language of concentration compactness theory [Kunze 2003], an extremizer f can be tight at a scale r , and f̂ can simultaneously be tight at a scale r̂ , with the product r · r̂ arbitrarily large.”
The geodesic X-ray transform with fold caustics (2010, background): “The presence of these symmetries among the extremizers for P2 implies that, in the language of concentration compactness theory [Kunze 2003], an extremizer f can be tight at a scale r , and f̂ can simultaneously be tight at a scale r̂ , with the product r · r̂ arbitrarily large.”
Maximizers for the Stein–Tomas Inequality (2016, unknown): “We feel that this approach is more direct than earlier approaches using Xp spaces, which were used in connection with refined Strichartz inequalities (and were also an ingredient in [23, 28]).”