Balinsky, Alexander; Ryan, John Some sharp \(L^2\) inequalities for Dirac type operators. (English) Zbl 1141.15026 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 114, 10 p. (2007). The stereographic projection corresponds to the Cayley transformation from \(S^{n}\mathbb N\) to the Euclidean space \(\mathbb{R}^{n}\), where \(N\) denotes the nord pole. The authors use this Cayley transformation to obtain some sharp \(L^2\) inequalities on the sphere for a family of Dirac type operators. The main tool is to employ a lowest eigenvalue for these operators and then use intertwining operators for the Dirac type operators to obtain analogous sharp inequalities in \(\mathbb{R}^{n}\). Reviewer: Georgi Hristov Georgiev (Shumen) Cited in 1 Document MSC: 15A66 Clifford algebras, spinors 26D10 Inequalities involving derivatives and differential and integral operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 15A45 Miscellaneous inequalities involving matrices Keywords:Dirac operator; Clifford algebra; conformal Laplacian; Cayley transformation; inequalities; lowest eigenvalue; intertwining operators PDFBibTeX XMLCite \textit{A. Balinsky} and \textit{J. Ryan}, SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 114, 10 p. (2007; Zbl 1141.15026) Full Text: DOI arXiv EuDML EMIS