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Topics in Clifford analysis. Special volume in honor of Wolfgang Sprößig on the occasion of his 70th birthday. (English) Zbl 1432.30001

Trends in Mathematics. Cham: Birkhäuser (ISBN 978-3-030-23853-7/hbk; 978-3-030-23854-4/ebook). xxi, 503 p. (2019).

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Publisher’s description: Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis.
The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
The articles of this volume will be reviewed individually.
Indexed articles:
Brackx, Fred; De Schepper, Hennie; Lávička, Roman; Souček, Vladimir, Cauchy’s formula in Clifford analysis: an overview, 3-23 [Zbl 1461.30114]
Eriksson, Sirkka-Liisa; Orelma, Heikki, Quaternionic hyperbolic function theory, 25-52 [Zbl 1442.30052]
Perotti, Alessandro, Slice regularity and harmonicity on Clifford algebras, 53-73 [Zbl 1442.30057]
Stoppato, Caterina, Some notions of subharmonicity over the quaternions, 75-101 [Zbl 1442.30059]
Marín, Juan José; Martell, José María; Mitrea, Dorina; Mitrea, Irina; Mitrea, Marius, A Fatou theorem and Poisson’s integral representation formula for elliptic systems in the upper half-space, 105-124 [Zbl 1442.35112]
Delgado, Briceyda B.; Porter, R. Michael, Hardy spaces for the three-dimensional Vekua equation, 125-140 [Zbl 1456.46025]
Brackx, Fred, Radial and angular derivatives of distributions, 141-171 [Zbl 1456.46038]
Cerejeiras, Paula; Kähler, Uwe; Kraußhar, R. Sören, Applications of parabolic Dirac operators to the instationary viscous MHD equations on conformally flat manifolds, 173-190 [Zbl 1442.35325]
Bernstein, Swanhild; Schufmann, Sandra, Generalized Riesz transforms, quasi-monogenic functions and frames, 191-218 [Zbl 1442.42037]
Gürlebeck, Klaus; Legatiuk, Dmitrii, Quaternionic operator calculus for boundary value problems of micropolar elasticity, 221-234 [Zbl 1443.74152]
Bock, Sebastian; Legatiuk, Dmitrii, Constructive orthonormalisation of monogenic polynomials on a finite cylinder, 235-250 [Zbl 1442.30050]
Morais, Joaõ, Comments on an orthogonal family of monogenic functions on spheroidal domains, 251-266 [Zbl 1442.30055]
Janovská, Drahoslava; Opfer, Gerhard, Newton’s approach to general algebraic equations over Clifford algebras, 267-276 [Zbl 1444.15011]
Abramov, Viktor; Liivapuu, Olga, Connections in Euclidean and non-commutative geometry, 279-311 [Zbl 1442.58009]
Kisil, Vladimir V.; Reid, James, Conformal parametrisation of loxodromes by triples of circles, 313-330 [Zbl 1450.30021]
Kraußhar, Rolf Sören, Automorphic forms and Dirac operators on conformally flat manifolds, 331-345 [Zbl 1442.30053]
Ding, Chao; Walter, Raymond; Ryan, John, Higher order fermionic and bosonic operators, 347-380 [Zbl 1444.15010]
Nolder, Craig A., Clifford Möbius geometry, 381-394 [Zbl 1442.30056]
Lávička, Roman, Separation of variables in the semistable range, 395-403 [Zbl 1498.30027]
Krasnov, Yakov; Tkachev, Vladimir G., Variety of idempotents in nonassociative algebras, 405-436 [Zbl 1477.17001]
Faustino, Nelson, Relativistic wave equations on the lattice: an operational perspective, 439-469 [Zbl 1451.39004]
Ren, Guangbin; Zhu, Zeping, Cauchy-Pompeiu formula for discrete monogenic functions, 471-486 [Zbl 1442.30058]
Hommel, Angela, A useful transformation for solving the discrete Beltrami equation and reducing a difference equation of second order to a system of equations of first order, 487-503 [Zbl 1442.39021]

MSC:

30-06 Proceedings, conferences, collections, etc. pertaining to functions of a complex variable
32-06 Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces
31-06 Proceedings, conferences, collections, etc. pertaining to potential theory
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
15A66 Clifford algebras, spinors
35Jxx Elliptic equations and elliptic systems
00B15 Collections of articles of miscellaneous specific interest
00B30 Festschriften

Biographic References:

Sprößig, Wolfgang
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