Clifford Analysis and Its ApplicationsF. Brackx, J.S.R. Chisholm, V. Soucek In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields. |
Contents
| 9 | |
T Branson | 27 |
J Bureš | 39 |
P Cerejeiras U Kähler | 49 |
JSR Chisholm | 59 |
SL ErikssonBique | 70 |
K Gürlebeck | 81 |
B Jancewicz | 91 |
HR Malonek | 212 |
A Axelsson R Grognard J Hogan A McIntosh | 231 |
H Liu J Ryan | 247 |
The Conformal Laplacian on Spheres and Hyperbolas via Clifford | 255 |
P Somberg | 292 |
F Sommen | 301 |
Souček | 321 |
W Sprößig | 340 |
Kadlčáková | 103 |
Communication via Holomorphic Green Functions 113 | 112 |
Physics 135 | 134 |
ford Analysis | 139 |
Krump | 155 |
Labunets E LabunetsRundblad J Astola | 172 |
H Leutwiler | 194 |
Sabadini F Sommen | 361 |
A Trautman | 377 |
P Van Lancker | 389 |
N Vasilevski | 400 |
List of Participants | 411 |
Other editions - View all
Clifford Analysis and Its Applications F. Brackx,John Stephen roy Chisholm,V. Soucek Limited preview - 2001 |
Clifford Analysis and Its Applications F. Brackx,John Stephen roy Chisholm,V. Soucek No preview available - 2001 |
Clifford Analysis and Its Applications F Brackx,J S R Chisholm,Vladimir Soucek No preview available - 2001 |
Common terms and phrases
2001 Kluwer Academic 60th birthday Applications BGG sequence boundary value problems Brackx bundle calculation Cauchy Cauchy-Riemann classical Clifford algebra Clifford analysis complex compute conformally invariant consider corresponding Dedicated to Richard defined denote differential forms differential operators dimensions Dirac operator domain double covers elements elliptic equation Euclidean field formula function f geometry Gürlebeck Hardy spaces harmonic Hilbert holomorphic homogeneous hypercomplex hyperholomorphic invariant operators isomorphism Kluwer Academic Publishers Kwaśniewski LEMMA linear Lipschitz Lipschitz domains Malonek manifold mapping Math Mathematics Subject Classification matrix Möbius transformations monogenic functions obtained orthogonal parallel transported Phys plane polynomial proof properties Qp-spaces quaternionic relation representation Riccati Riccati equation Richard Delanghe satisfying scalar singular integral singular integral operators solutions Sommen space spin spin group spinor subspace symplectic tensor theorem theory transform vector variables wavelet მე მყ