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Dispersive and Strichartz estimates on H-type groups

Martin Del Hierro (2005)

Studia Mathematica

Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as t - p / 2 ) and the Schrödinger equation (decay as t ( 1 - p ) / 2 ), p being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that p > 1, for the Schrödinger equation.

Distributions of truncations of the heat kernel on the complex projective space

Nizar Demni (2014)

Annales mathématiques Blaise Pascal

Let ( U t ) t ≥ 0 be a Brownian motion valued in the complex projective space ℂ P N - 1 . Using unitary spherical harmonics of homogeneous degree zero, we derive the densities of | U t 1 | 2 and of ( | U t 1 | 2 , | U t 2 | 2 ) , and express them through Jacobi polynomials in the simplices of ℝ and ℝ 2 respectively. More generally, the distribution of ( | U t 1 | 2 , ⋯ , | U t k | 2 ) , 2 ≤ k ≤ N - 1 may be derived using the decomposition of the unitary spherical harmonics under the action of the unitary group 𝒰 ( N - k + 1 ) yet computations become tedious. We also revisit the approach initiated in [13] and based on...

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