1. Quaternionic Analysis.- 1.1. Algebra of Real Quaternions.- 1.2. H-regular Functions.- 1.3. A Generalized LEIBNIZ Rule.- 1.4. BOREL-POMPEIU s Formula.- 1.5. Basic Statements of H-regular Functions.- 2. Operators.- 2.3. Properties of the T-Operator.- 2.4. VEKUA 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 DIRICHLET 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.
Inhaltsverzeichnis
1. Quaternionic Analysis. - 1. 1. Algebra of Real Quaternions. - 1. 2. H-regular Functions. - 1. 3. A Generalized LEIBNIZ Rule. - 1. 4. BOREL-POMPEIU s Formula. - 1. 5. Basic Statements of H-regular Functions. - 2. Operators. - 2. 3. Properties of the T-Operator. - 2. 4. VEKUA 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 DIRICHLET 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.
