Die Funktionentheorie einer komplexen Variablen hat heute hC6her-dimensionale Analoga: dabei wird die Algebra der komplexen Zahlen durch die nicht-kommutative Algebra der reellen Quaternionen bzw. Clifford-Algebren ersetzt. In den letzten 30 Jahren hat sich die so genannte Quaternionen- und die reelle Clifford-Analysis erfolgreich entwickelt. Eine Vielzahl von Anwendungen haben diese Funktionentheorie hC6her-dimensionaler Variablen zu einem wichtigen Instrument der Analysis und deren Anwendungen in der mathematischen Physik werden lassen. Das Buch reflektiert den neuesten Stand der Forschung...
Die Funktionentheorie einer komplexen Variablen hat heute hC6her-dimensionale Analoga: dabei wird die Algebra der komplexen Zahlen durch die nicht-kom...
Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.
Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real qu...
This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and...
This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical p...
