Clifford analysis

Clifford analysis, using Clifford algebras named after William Kingdon Clifford, is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators include, but are not limited to, the Hodge–Dirac operator, d + ⋆ d ⋆ {displaystyle d+{star }d{star }} on a Riemannian manifold, the Dirac operator in euclidean space and its inverse on C 0 ∞ ( R n ) {displaystyle C_{0}^{infty }(mathbf {R} ^{n})} and their conformal equivalents on the sphere, the Laplacian in euclidean n-space and the Atiyah–Singer–Dirac operator on a spin manifold, Rarita–Schwinger/Stein–Weiss type operators, conformal Laplacians, spinorial Laplacians and Dirac operators on Spinc manifolds, systems of Dirac operators, the Paneitz operator, Dirac operators on hyperbolic space, the hyperbolic Laplacian and Weinstein equations. Clifford analysis, using Clifford algebras named after William Kingdon Clifford, is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators include, but are not limited to, the Hodge–Dirac operator, d + ⋆ d ⋆ {displaystyle d+{star }d{star }} on a Riemannian manifold, the Dirac operator in euclidean space and its inverse on C 0 ∞ ( R n ) {displaystyle C_{0}^{infty }(mathbf {R} ^{n})} and their conformal equivalents on the sphere, the Laplacian in euclidean n-space and the Atiyah–Singer–Dirac operator on a spin manifold, Rarita–Schwinger/Stein–Weiss type operators, conformal Laplacians, spinorial Laplacians and Dirac operators on Spinc manifolds, systems of Dirac operators, the Paneitz operator, Dirac operators on hyperbolic space, the hyperbolic Laplacian and Weinstein equations.