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Clifford analysis and related topics. In honor of Paul A. M. Dirac, CART 2014, Tallahassee, Florida, December 15–17, 2014. (English) Zbl 1403.15001

Springer Proceedings in Mathematics & Statistics 260. Cham: Springer (ISBN 978-3-030-00047-9/hbk; 978-3-030-00049-3/ebook). vii, 152 p. (2018).

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Publisher’s description: This book, intended to commemorate the work of Paul Dirac, highlights new developments in the main directions of Clifford analysis. Just as complex analysis is based on the algebra of the complex numbers, Clifford analysis is based on the geometric Clifford algebras. Many methods and theorems from complex analysis generalize to higher dimensions in various ways. However, many new features emerge in the process, and much of this work is still in its infancy.
Some of the leading mathematicians working in this field have contributed to this book in conjunction with “Clifford analysis and related topics: a conference in honor of Paul A.M. Dirac,” which was held at Florida State University, Tallahassee, on December 15–17, 2014. The content reflects talks given at the conference, as well as contributions from mathematicians who were invited but were unable to attend. Hence much of the mathematics presented here is not only highly topical, but also cannot be found elsewhere in print. Given its scope, the book will be of interest to mathematicians and physicists working in these areas, as well as students seeking to catch up on the latest developments.
The articles of this volume will be reviewed individually.
Indexed articles:
Ballenger-Fazzone, K.; Nolder, C. A., Lambda-harmonic functions: an expository account, 1-17 [Zbl 1404.35118]
Cerejeiras, P.; Kähler, U.; Kraußhar, R. S., Some applications of parabolic Dirac operators to the instationary Navier-Stokes problem on conformally flat cylinders and tori in \(\mathbb {R}^3\), 19-37 [Zbl 1405.35135]
Cerejeiras, P.; Kähler, U.; Ryan, J., From Hermitean Clifford analysis to subelliptic Dirac operators on odd dimensional spheres and other CR manifolds, 39-51 [Zbl 1402.35089]
Ding, C.; Ryan, J., On some conformally invariant operators in Euclidean space, 53-72 [Zbl 1402.30044]
Emanuello, J. A.; Nolder, C. A., Notions of regularity for functions of a split-quaternionic variable, 73-96 [Zbl 1403.30018]
Raeymaekers, T., Decomposition of the twisted Dirac operator, 97-111 [Zbl 1406.35315]
Vajiac, M. B., Norms and moduli on multicomplex spaces, 113-140 [Zbl 1426.30037]
Vanegas, C. J.; Vargas, F. A., Associated operators to the space of meta-\(q\)-monogenic functions, 141-152 [Zbl 1402.35078]

MSC:

15-06 Proceedings, conferences, collections, etc. pertaining to linear algebra
15A66 Clifford algebras, spinors
00B15 Collections of articles of miscellaneous specific interest
00B25 Proceedings of conferences of miscellaneous specific interest

Biographic References:

Dirac, Paul A. M.
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