Introduction to Clifford analysis : a new perspective
著者
書誌事項
Introduction to Clifford analysis : a new perspective
（Mathematics research developments series）
Nova Science Publishers, c2020
- pbk.
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注記
Includes bibliographical references (p. [155]-163) and index
Other authors: Nicolás Coloma, Antonio Di Teodoro, Francisco Ponce
内容説明・目次
内容説明
This book pursues to exhibit how we can construct a Clifford type algebra from the classical one. The basic idea of these lecture notes is to show how to calculate fundamental solutions to either firstorder differential operators of the form D=∑_(i=0)^n▒〖e_i δ_i〗or secondorder elliptic differential operators¯D D, both with constant coefficients or combinations of this kind of operators. After considering in detail how to find the fundamental solution we study the problem of integral representations in a classical Clifford algebra and in a dependentparameter Clifford algebra which generalizes the classical one. We also propose a basic method to extend the order of the operator, for instance D^n,n∈N and how to produce integral representations for higher order operators and mixtures of them. Although the Clifford algebras have produced many applications concerning boundary value problems, initial value problems, mathematical physics, quantum chemistry, among others; in this book we do not discuss these topics as they are better discussed in other courses. Researchers and practitioners will find this book very useful as a source book. The reader is expected to have basic knowledge of partial differential equations and complex analysis. When planning and writing these lecture notes, we had in mind that they would be used as a resource by mathematics students interested in understanding how we can combine partial differential equations and Clifford analysis to find integral representations. This in turn would allow them to solve boundary value problems and initial value problems. To this end, proofs have been described in rigorous detail and we have included numerous worked examples. On the other hand, exercises have not been included.
目次
- Preface
- Complex Numbers
- ComplexValued Functions
- Clifford Algebras and CauchyRiemann Operator
- Short Introduction to Clifford Analysis
- Matrix Representation
- Fundamental Solution for the CauchyRiemann operator
- Clifford Type Algebras
- Fun-damental Solution D_λ
- Fundamental Solution for the Second Order Operator
- Distributional Solutions
- Applications Associated to Operators Dand ∆ þ
- MultiDimensional Clifford Type Algebras
- Clifford Fractional Operators
- Appendix.
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