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Spectral projections and resolvent estimates on Damek–Ricci spaces and their applications

Year: 2026

Type: article

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.

Source: Forum Mathematicum

DOI: 10.1515/forum-2024-0588

Authors: Mithun Bhowmik, Utsav Dewan

Institutions: Indian Institute of Technology Kharagpur, Indian Institute of Technology Bombay

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Indian Statistical Institute

OpenAlex ID: W4380558559

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