Analysis seminar
IPDF talk
Friday, 2nd Feb. 4 pm - 5 pm
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Venue: Online, link TBA
Host: Sanjay Pusti
Speaker: Jitendra Kumar Senapati
Affiliation : BITS Pilani, Goa
Title: Restriction theorem for the Fourier-Dunkl transform and its applications to Strichartz inequalities
Abstract: We define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz’s restriction theorem for the Fourier-Dunkl transform for certain surfaces, namely, cone, paraboloid, sphere, and hyperboloid, and its generalization to the family of orthonormal functions. Finally, as an application of these restriction theorems, we establish versions of Strichartz estimates for orthonormal families of initial data associated with the Schrodinger propagator, wave propagator, and Klein-Gordon propagator for the case of the Dunkl Laplacian. This restriction theorem generalizes Stein-Tomas and Strichartz’s restrictions theorems in special cases. This is a joint work with B. Pradeep, S. S. Mondal, and H. Mejjaoli.