Spectral projections and resolvent estimates on Damek–Ricci spaces and their applications
Abstract
Abstract We prove L p - L p ′ {L^{p}-L^{p^{\prime}}} boundedness of spectral projections and the resolvent of the Laplace–Beltrami operator on Damek–Ricci spaces with the explicit norms in terms of the spectral parameter. To prove these results we established pointwise sharp bounds on the spherical functions and their derivatives. As an application, we study the eigenvalue bounds of Schrödinger operators with complex valued potential.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Forum Mathematicum
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 25 June 2026
- Language
- EN