Klaus Habetha's Books

Holomorphic Functions in the Plane and n-dimensional Space

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

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Holomorphic Functions in the Plane and n-dimensional Space

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

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.

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Page Count

407

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764382724

ISBN 13

9783764382728

Application of Holomorphic Functions in Two and Higher Dimensions

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

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Application of Holomorphic Functions in Two and Higher Dimensions

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

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 different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.

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Page Count

402

Publisher

Springer

Published Date

ISBN 10

3034809646

ISBN 13

9783034809641

Holomorphic Functions in the Plane and n-dimensional Space

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

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Holomorphic Functions in the Plane and n-dimensional Space

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

407

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764382724

ISBN 13

9783764382728

Application of Holomorphic Functions in Two and Higher Dimensions

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

Write a review Read reviews Take a Quiz Solve Book Puzzle

Application of Holomorphic Functions in Two and Higher Dimensions

By: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

402

Publisher

Springer

Published Date

ISBN 10

3034809646

ISBN 13

9783034809641

Book's by Klaus Habetha

Holomorphic Functions in the Plane and n-dimensional Space

Holomorphic Functions in the Plane and n-dimensional Space

Application of Holomorphic Functions in Two and Higher Dimensions

Application of Holomorphic Functions in Two and Higher Dimensions

Holomorphic Functions in the Plane and n-dimensional Space

Holomorphic Functions in the Plane and n-dimensional Space

Application of Holomorphic Functions in Two and Higher Dimensions

Application of Holomorphic Functions in Two and Higher Dimensions

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