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目次

IntroductionPrinciples of Clifford Algebra and AnalysisThe Basic Notions and DefinitionsMatrix Representations of Clifford Algebras for any DimensionDifferential Operators and ClassificationLorentz Transformations in the Elliptic and Hyperbolic CasesElliptic Partial Differential EquationsIntroductionCauchy Kernel and Representations for h-regular Functions in R(n)Extension Theorems and The Riemann-Schwarz Principle of ReflectionThe Poincaré-Bertrand Transformation FormulaGeneralized Riesz SystemThe Basic L-Theory of the Fourier Integral TransformationBoundary Value Problems for Regular Functions with Values in R(n)Boundary Value Problems for h-Regular Functions with Values in R(n), n³1The Beltrami Equation in R(n)Hyperbolic Partial Differential EquationsIntroductionGeneralized Maxwell and Dirac EquationsThe Hyperbolic Beltrami EquationInitial Value Problems for the Klein-Gordon EquationCauchy's Initial Value Problem and its Modification for the Regular and h-Regular Functions with Values in R(n,n-1) and in R(n,n-2), n³3Parabolic Partial Differential EquationsIntroductionParabolic Regular System of the First KindInitial Value Problems for Parabolic Equations of the First KindParabolic Regular Equations of the Second Kind and Initial Value ProblemsEffective Solutions for Some Non-Local ProblemsIntroductionWiener-Hopf and Dual Integral Equations of Convolution TypeGeneralized Wiener-Hopf Integral Equation with Two Kernels Depending on the Difference and Sum of the ArgumentsDual Integral Equations with Kernels Depending on the Difference and Sum of ArgumentsNon-Local Problems for Holomorphic Functions and Applications in Elasticity TheoryNon-Local Problems for Generalized Holomorphic Functions and the Generalized Beltrami EquationNon-Local Problems for Polyharmonic FunctionsEpilogueBibliography