Holomorphic Functions in the Plane and n-dimensional SpaceComplex 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. |
Contents
1 | 3 |
4 | 33 |
Multilinear products | 42 |
3 | 50 |
II | 72 |
3 | 104 |
2 | 111 |
3 | 124 |
10 | 186 |
11 | 216 |
2 | 225 |
Differential forms in | 324 |
1 2 | 338 |
Properties of holomorphic spherical functions | 363 |
| 377 | |
| 385 | |
Other editions - View all
Holomorphic Functions in the Plane and n-dimensional Space Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig No preview available - 2009 |
Common terms and phrases
Am,n analogous arbitrary automorphic basis elements Bm,n boundary C¹(G calculated called Cauchy Cauchy's integral formula Cauchy's integral theorem Cl(n Clifford algebra Clp,q Cm,n coefficients complex numbers continuous Corollary corresponding cosh curve defined Definition denoted derivatives differential equations differential form domain G Eisenstein series Example Exercise finite follows Fueter polynomials function f geometric given H-holomorphic higher dimensions Hölder holds holomorphic function integral theorem Laurent series left-holomorphic Let f linear manifold mapping matrix meromorphic Möbius transformations multiplication obtain operator orthogonal paravector piecewise smooth plane poles power series Proof properties Proposition prove quaternions R²+¹ radius real numbers Remark representation residue resp Riemann Riemann sphere Rn+1 rotation scalar product sequence singularity sinh sphere spherical functions Taylor series variables vector product vector space xn+1 zero ση