Pseudoconformal Transformation: Difference between revisions

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The pseudoconformal transformation
The pseudoconformal transformation


<math> u(t,x) \to v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{i |y|^2}{4t} u ( - \frac{1}{\tau} , \frac{y}{\tau}) </math>
<math> u(t,x) \to v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{\frac{i |y|^2}{4t}} u ( - \frac{1}{\tau} , \frac{y}{\tau}) </math>


maps solutions of the [[Mass critical NLS|mass critical NLS]] to solutions. The pseudoconformal image of a [[Soliton|soliton]] is an explicit [[Blowup solution|blowup solution]]. The pseudoconformal transformation is an isometry on <math>L^2_x</math> and on <math>L^2</math>-admissible [[Strichartz estimates|Strichartz spaces]] <math>L^q_\tau L^r_y</math>.
maps solutions of the [[Mass critical NLS|mass critical NLS]] to solutions. The pseudoconformal image of a [[Soliton|soliton]] is an explicit [[Blowup solution|blowup solution]]. The pseudoconformal transformation is an isometry on <math>L^2_x</math> and on <math>L^2</math>-admissible [[Strichartz estimates|Strichartz spaces]] <math>L^q_\tau L^r_y</math>.

Revision as of 02:03, 31 July 2006

The pseudoconformal transformation

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle u(t,x) \to v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{\frac{i |y|^2}{4t}} u ( - \frac{1}{\tau} , \frac{y}{\tau}) }

maps solutions of the mass critical NLS to solutions. The pseudoconformal image of a soliton is an explicit blowup solution. The pseudoconformal transformation is an isometry on and on -admissible Strichartz spaces .