Schrodinger Equations on Damek-Ricci Spaces

被引：16

作者：

Anker, Jean-Philippe ^{[1
,2
,3
]}

Pierfelice, Vittoria ^{[1
,2
,3
]}

Vallarino, Maria ^{[4
]}

机构：

[1] Lab MAPMO, UMR 6628, F-45067 Orleans 2, France

[2] Univ Orleans, Orleans, France

[3] CNRS, Federat Denis Poisson FR 2964, F-45071 Orleans, France

[4] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Milan, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 36卷 / 06期

关键词：

Damek-Ricci spaces; Dispersive estimate; Heat kernel estimate; Schrodinger equation; Strichartz estimate; NONCOMPACT SYMMETRIC-SPACES; LAPLACE-BELTRAMI OPERATOR; HYPERBOLIC SPACE; SINGULAR-INTEGRALS; WAVE-EQUATION; STRICHARTZ INEQUALITIES; SPECTRAL MULTIPLIERS; EXPONENTIAL-GROWTH; HEAT KERNEL; MANIFOLDS;

D O I：

10.1080/03605302.2010.539658

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the Laplace-Beltrami operator on Damek-Ricci spaces and derive pointwise estimates for the kernel of e, when * with Re epsilon 0. When i*, we obtain in particular pointwise estimates of the Schrodinger kernel associated with . We then prove Strichartz estimates for the Schrodinger equation, for a family of admissible pairs which is larger than in the Euclidean case. This extends the results obtained by Anker and Pierfelice [4] on real hyperbolic spaces. As a further application, we study the dispersive properties of the Schrodinger equation associated with a distinguished Laplacian on Damek-Ricci spaces, showing that in this case the standard L1L estimate fails while suitable weighted Strichartz estimates hold.

引用

页码：976 / 997

页数：22

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