Clifford Analysis

Clifford analysis......Page 1
Contents......Page 4
List of symbols......Page 6
Preface......Page 11
1. Clifford numbers......Page 14
2. Modules over Clifford algebras: general properties......Page 26
3. The spaces Cº(K;A) and Cº(Ω;A); A-measures......Page 36
4. The space D(Ω;A); A-distributions......Page 38
5. The space S(Rr,A); tempered A-distributions......Page 45
6. The space E(Ω;A); A-distributions with compact support......Page 47
7. Hilbert A-modules......Page 48
Notes to Chapter 1......Page 53
Bibliography......Page 54
8. A decomposition of the Laplace and Laplace-Beltrami operator......Page 57
9. Cauchy\'s integral formula and its applications......Page 64
10. Morera\'s Theorem......Page 73
11. Taylor series......Page 78
12. Laurent series and pointwise singularities......Page 97
13. Adjoint monogenic functions......Page 115
14. A product of monogenic functions......Page 121
15. Elementary monogenic functions......Page 128
Notes to Chapter 2......Page 150
Bibliography......Page 152
16. The space M(r)(Ω;A)......Page 155
17. The space M~(r)(Ω;A)......Page 156
18. Runge type theorems......Page 163
19. The equation Df = g......Page 173
20. Primitives of monogenic functions......Page 178
21. Mittag-Leffler theorems......Page 180
22. The dual of M(r)(Ω;A)......Page 182
23. The bidual of M(r)(Ω;A)......Page 194
24. Hilbert modules with reproducing kernel......Page 197
Notes to Chapter 3......Page 206
Bibliography......Page 208
25. Distributional extension properties of harmonic functions......Page 212
26. Distributional boundary values and canonical extensions of monogenic functions......Page 216
27. Representation of distributions by monogenic functions......Page 223
28. Analytic functions and functionals on the unit sphere......Page 228
29. L2-Functions on the unit sphere - the Szegö and Bergmann kernels......Page 237
Notes to Chapter 4......Page 251
Bibliography......Page 254
5. Transform analysis in Euclidean space......Page 257
30. Hypercomplex Fourier transforms......Page 258
31. The generalized Laplace transform in S*(1)(Rm;A)......Page 266
32. A generalized Fourier-Borel transform......Page 278
33. Connections with complex analysis - a generalized Radon transform......Page 297
Notes to Chapter 5......Page 310
Bibliography......Page 313
References......Page 315
Author index......Page 317
Index......Page 319