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AuthorGรผrlebeck, Klaus. author
TitleQuaternionic Analysis and Elliptic Boundary Value Problems [electronic resource] / by Klaus Gรผrlebeck, Wolfgang Sprรถร{159}ig
ImprintBasel : Birkhรคuser Basel, 1989
Connect tohttp://dx.doi.org/10.1007/978-3-0348-7295-9
Descript 254 p. online resource

CONTENT

1. Quaternionic Analysis -- 1.1. Algebra of Real Quaternions -- 1.2. H-regular Functions -- 1.3. A Generalized LEIBNIZ Rule -- 1.4. BOREL-POMPEIUโ{128}{153}s Formula -- 1.5. Basic Statements of H-regular Functions -- 2. Operators -- 2.3. Properties of the T-Operator -- 2.4. VEKUAโ{128}{153}s Theorems -- 2.5. Some Integral Operators on the Manifold -- 3. Orthogonal Decomposition of the Space L2,H(G) -- 4. Some Boundary Value Problems of DIRICHLETโ{128}{153}s Type -- 4.1. LAPLACE Equation -- 4.2. HELMHOLTZ Equation -- 4.3. Equations of Linear Elasticity -- 4.4. Time-independent MAXWELL Equations -- 4.5. STOKES Equations -- 4.6. NAVIER-STOKES Equations -- 4.7. Stream Problems with Free Convection -- 4.8. Approximation of STOKES Equations by Boundary Value Problems of Linear Elasticity -- 5. H-regular Boundary Collocation Methods -- 5.1. Complete Systems of H-regular Functions -- 5.2. Numerical Properties of H-complete Systems of H-regular Functions -- 5.3. Foundation of a Collocation Method with H-regular Functions for Several Elliptic Boundary Value Problems -- 5.4. Numerical Examples -- 6. Discrete Quaternionic Function Theory -- 6.1. Fundamental Solutions of the Discrete Laplacian -- 6.2. Fundamental Solutions of a Discrete Generalized CAUCHY-RIEMANN Operator -- 6.3. Elements of a Discrete Quaternionic Function Theory -- 6.4. Main Properties of Discrete Operators -- 6.5. Numerical Solution of Boundary Value Problems of NAVIER-STOKES Equations -- 6.6. Concluding Remarks -- References -- Notations


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