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Author ID: sommen.franciscus Recent zbMATH articles by "Sommen, Franciscus"
Published as: Sommen, F.; Sommen, Frank; Sommen, Franciscus; Sommen, Frank C.; Sommen, Fransiscus; Sommen, F. C.
Homepage: https://biblio.ugent.be/person/801000476064
External Links: MGP · ResearchGate · Math-Net.Ru · dblp · GND
Documents Indexed: 295 Publications since 1979, including 4 Books
6 Contributions as Editor
Biographic References: 1 Publication
Co-Authors: 62 Co-Authors with 245 Joint Publications
805 Co-Co-Authors
all top 5

Serials

26 Advances in Applied Clifford Algebras
17 Mathematical Methods in the Applied Sciences
17 Complex Analysis and Operator Theory
15 Journal of Mathematical Analysis and Applications
12 Complex Variables. Theory and Application
7 Journal of Natural Geometry
7 Complex Variables and Elliptic Equations
6 Zeitschrift für Analysis und ihre Anwendungen
5 Results in Mathematics
5 Bulletin of the Belgian Mathematical Society - Simon Stevin
5 Integral Transforms and Special Functions
5 Communications on Pure and Applied Analysis
5 Journal of Physics A: Mathematical and Theoretical
5 Trends in Mathematics
4 Journal of Mathematical Physics
4 Journal of Geometry and Physics
4 Applied Mathematics and Computation
4 Simon Stevin
4 The Journal of Fourier Analysis and Applications
4 Boundary Value Problems
4 Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II
3 Applicable Analysis
3 Archiv der Mathematik
3 Journal of Approximation Theory
3 Mathematische Zeitschrift
3 Acta Mathematica Sinica. English Series
3 Cubo
2 Bulletin de la Société Royale des Sciences de Liège
2 International Journal of Mathematics and Mathematical Sciences
2 Journal of Functional Analysis
2 Mathematische Nachrichten
2 Tokyo Journal of Mathematics
2 Bulletin de la Société Matheḿatique de Belgique. Série B
2 The Journal of Geometric Analysis
2 Experimental Mathematics
2 Computational Methods and Function Theory
2 Bulletin of the Brazilian Mathematical Society. New Series
1 Computers & Mathematics with Applications
1 Inverse Problems
1 Israel Journal of Mathematics
1 Journal d’Analyse Mathématique
1 Arkiv för Matematik
1 Annales Polonici Mathematici
1 Bulletin of the London Mathematical Society
1 Czechoslovak Mathematical Journal
1 Illinois Journal of Mathematics
1 Integral Equations and Operator Theory
1 Journal of the London Mathematical Society. Second Series
1 Journal of the Mathematical Society of Japan
1 Journal für die Reine und Angewandte Mathematik
1 Mathematical Journal of Okayama University
1 Portugaliae Mathematica
1 Proceedings of the American Mathematical Society
1 Proceedings of the London Mathematical Society. Third Series
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Transactions of the American Mathematical Society
1 Advances in Applied Mathematics
1 Chinese Annals of Mathematics. Series B
1 Scientific Papers of the College of Arts and Sciences
1 Annals of Global Analysis and Geometry
1 Constructive Approximation
1 Annals of Physics
1 Proceedings of the Royal Irish Academy. Section A, Mathematical and Physical Sciences
1 Journal of Mathematical Imaging and Vision
1 Methods and Applications of Analysis
1 Journal of Difference Equations and Applications
1 Moscow Mathematical Journal
1 Journal of Analysis and Applications
1 Analysis and Applications (Singapore)
1 Mathematics and its Applications (Dordrecht)
1 Seminari di Geometria. Universitá degli Studi di Bologna
1 Chapman & Hall/CRC Research Notes in Mathematics
1 Progress in Mathematical Physics
1 Communications in Mathematical Analysis
1 Springer INdAM Series
1 Research Notes in Mathematics (San Francisco)

Publications by Year

Citations contained in zbMATH Open

241 Publications have been cited 3,154 times in 1,105 Documents Cited by Year
Clifford analysis. Zbl 0529.30001
Brackx, F.; Delanghe, R.; Sommen, F.
485
1982
Clifford algebra and spinor-valued functions. A function theory for the Dirac operator. Related REDUCE software by F. Brackx and D. Constales. Zbl 0747.53001
Delanghe, R.; Sommen, F.; Souček, V.
356
1992
Analysis of Dirac systems and computational algebra. Zbl 1064.30049
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus; Struppa, Daniele C.
137
2004
Fundaments of Hermitean Clifford analysis. I: Complex structure. Zbl 1131.30019
Brackx, Fred; Bureš, Jarolím; De Schepper, Hennie; Eelbode, David; Sommen, Frank; Souček, Vladímir
61
2007
Fundaments of Hermitean Clifford analysis. II: Splitting of \(h\)-monogenic equations. Zbl 1144.30019
Brackx, F.; Bureš, J.; de Schepper, H.; Eelbode, D.; Sommen, F.; Souček, V.
58
2007
Special functions in Clifford analysis and axial symmetry. Zbl 0634.30042
Sommen, F.
53
1988
The Hermitian Clifford analysis toolbox. Zbl 1177.30064
Brackx, Fred; De Schepper, Hennie; Sommen, Frank
53
2008
Hermitian Clifford analysis and resolutions. Zbl 1013.30033
Sabadini, Irene; Sommen, Frank
51
2002
The Clifford-Fourier transform. Zbl 1122.42015
Brackx, Fred; De Schepper, Nele; Sommen, Frank
49
2005
The Fueter mapping theorem in integral form and the \(\mathcal F\)-functional calculus. Zbl 1225.47019
Colombo, Fabrizio; Sabadini, Irene; Sommen, Frank
45
2010
Rarita-Schwinger type operators in Clifford analysis. Zbl 1078.30041
Bureš, J.; Sommen, F.; Souček, V.; van Lancker, P.
38
2001
Spherical harmonics and integration in superspace. Zbl 1143.30315
De Bie, H.; Sommen, F.
38
2007
Lie groups as spin groups. Zbl 0810.15014
Doran, C.; Hestenes, D.; Sommen, F.; Van Acker, N.
37
1993
On a generalization of Fueter’s theorem. Zbl 1030.30039
Sommen, F.
37
2000
Models for irreducible representations of Spin\((m)\). Zbl 1221.22016
van Lancker, P.; Sommen, Frank; Constales, D.
32
2001
Integral theorems for functions and differential forms in \(C^m\). Zbl 0991.32002
Rocha-Chávez, Reynaldo; Shapiro, Michael; Sommen, Franciscus
30
2002
The two-dimensional Clifford-Fourier transform. Zbl 1122.42016
Brackx, Fred; De Schepper, Nele; Sommen, Frank
30
2006
Generalizations of Fueter’s theorem. Zbl 1079.30066
Kou, K. I.; Qian, T.; Sommen, F.
30
2002
On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis. Zbl 1182.30081
Brackx, F.; De Knock, B.; De Schepper, H.; Sommen, F.
29
2009
Discrete Dirac operators in Clifford analysis. Zbl 1208.30046
Faustino, Nelson; Kähler, Uwe; Sommen, Frank
27
2007
Symmetric analogues of Rarita-Schwinger equations. Zbl 1025.58013
Bureš, J.; Sommen, F.; Souček, V.; Van Lancker, P.
26
2002
Plane elliptic systems and monogenic functions in symmetric domains. Zbl 0564.30036
Sommen, F.
26
1984
Parabolic Dirac operators and the Navier-Stokes equations over time-varying domains. Zbl 1082.30039
Cerejeiras, P.; Káhle, U.; Sommen, F.
25
2005
The inverse Fueter mapping theorem. Zbl 1258.30022
Colombo, Fabrizio; Sabadini, Irene; Sommen, Frank
25
2011
Complexes of Dirac operators in Clifford algebras. Zbl 1078.30045
Sabadini, Irene; Struppa, Daniele C.; Sommen, Frank; Van Lancker, Peter
24
2002
Discrete function theory based on skew Weyl relations. Zbl 1201.30062
De Ridder, Hilde; De Schepper, Hennie; Kähler, Uwe; Sommen, Frank
24
2010
On conjugate harmonic functions in Euclidean space. Zbl 1056.30049
Brackx, F. F.; Delanghe, R.; Sommen, F. C.
23
2002
Correct rules for Clifford calculus on superspace. Zbl 1129.30034
De Bie, Hendrik; Sommen, Frank
22
2007
Spherical monogenic functions and analytic functionals on the unit sphere. Zbl 0481.30040
Sommen, Fransiscus
22
1981
A product and an exponential function in hypercomplex function theory. Zbl 0454.30039
Sommen, F.
20
1981
Quaternionic Clifford analysis: the Hermitian setting. Zbl 1211.30057
Peña-Peña, Dixan; Sabadini, Irene; Sommen, Frank
19
2007
A theoretical framework for wavelet analysis in a Hermitean Clifford setting. Zbl 1149.30036
Brackx, Fred; De Schepper, Hennie; Sommen, Frank
18
2007
Spherical harmonics and integration in superspace: II. Zbl 1179.30053
De Bie, H.; Eelbode, D.; Sommen, F.
18
2009
An alternative proof of Fueter’s theorem. Zbl 1117.30039
Peña Peña, Dixan; Qian, Tao; Sommen, Frank
18
2006
Deriving harmonic functions in higher dimensional spaces. Zbl 1052.30055
Qian, T.; Sommen, F.
18
2003
Differential forms and/or multi-vector functions. Zbl 1105.58002
Brackx, F.; Delanghe, R.; Sommen, F.
18
2005
Fischer decomposition by inframonogenic functions. Zbl 1217.30047
Malonek, Helmuth R.; Peña Peña, Dixan; Sommen, Frank
18
2010
Some connections between Clifford analysis and complex analysis. Zbl 0464.30039
Sommen, F.
17
1982
Hypercomplex Fourier and Laplace transforms. I. Zbl 0472.46032
Sommen, F.
17
1982
The class of Clifford-Fourier transforms. Zbl 1237.30017
De Bie, Hendrik; De Schepper, Nele; Sommen, Frank
17
2011
Clifford-Hermite wavelets in Euclidean space. Zbl 0961.42021
Brackx, F.; Sommen, F.
16
2000
Integration in superspace using distribution theory. Zbl 1187.58011
Coulembier, K.; de Bie, H.; Sommen, F.
16
2009
Cauchy integral formulae in quaternionic Hermitean Clifford analysis. Zbl 1275.30017
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
16
2012
A Clifford analysis approach to superspace. Zbl 1132.81017
De Bie, H.; Sommen, F.
15
2007
Discrete Clifford analysis: a germ of function theory. Zbl 1173.30034
Brackx, F.; De Schepper, H.; Sommen, F.; Van de Voorde, L.
15
2009
Clifford analysis and integral geometry. Zbl 0765.53073
Sommen, F.
14
1992
Fundamental solutions for operators which are polynomials in the Dirac operator. Zbl 0769.35053
Sommen, F.; Xu, Zhenyuan
14
1992
A basic framework for discrete Clifford analysis. Zbl 1186.30044
de Schepper, Hennie; Sommen, Frank; van de Voorde, Liesbet
14
2009
An algebra of abstract vector variables. Zbl 0886.15037
Sommen, F.
14
1997
A Cauchy-Kowalevski theorem for inframonogenic functions. Zbl 1235.30031
Malonek, Helmuth R.; Peña Peña, Dixan; Sommen, Frank
14
2011
Segal-Bargmann-Fock modules of monogenic functions. Zbl 1377.30043
Peña Peña, Dixan; Sabadini, Irene; Sommen, Franciscus
14
2017
The inverse Fueter mapping theorem in integral form using spherical monogenics. Zbl 1341.30042
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
14
2013
A Martinelli-Bochner formula for the Hermitian Dirac equation. Zbl 1117.30040
Sommen, Frank; Peña-Peña, Dixan
13
2007
Axial monogenic functions from holomorphic functions. Zbl 0802.30001
Common, A. K.; Sommen, F.
13
1993
Discrete Hardy spaces. Zbl 1308.44002
Cerejeiras, Paula; Kähler, Uwe; Ku, Min; Sommen, Frank
13
2014
Fueter polynomials in discrete Clifford analysis. Zbl 1258.30024
De Ridder, H.; De Schepper, H.; Sommen, F.
12
2012
Clifford analysis in two and several vector variables. Zbl 1054.30050
Sommen, F.
12
1999
Monogenic differential operators. Zbl 0765.30033
Sommen, F.; Van Acker, N.
12
1992
Fundamental solutions for the super Laplace and Dirac operators and all their natural powers. Zbl 1143.30022
De Bie, H.; Sommen, F.
12
2008
Twisted plane wave expansions using hypercomplex methods. Zbl 1288.30051
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus; Struppa, Daniele C.
12
2014
Spherical means and distributions in Clifford analysis. Zbl 1058.30043
Brackx, Fred; Delanghe, Richard; Sommen, Frank
11
2004
Martinelli-Bochner formula using Clifford analysis. Zbl 1114.30052
Sommen, Frank; Peña, Dixan Peña
11
2007
Spherical means, distributions and convolution operators in Clifford analysis. Zbl 1056.30050
Brackx, F.; Delanghe, R.; Sommen, F.
11
2003
Boundary value problems associated to a Hermitian Helmholtz equation. Zbl 1269.30050
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
11
2012
Hypercomplex Fourier and Laplace transforms. II. Zbl 0529.46030
Sommen, F.
11
1983
Microfunctions with values in a Clifford algebra. II. Zbl 0649.30040
Sommen, Franciscus
11
1986
Clifford analysis, biaxial symmetry and pseudoanalytic functions. Zbl 0703.30044
Jank, G.; Sommen, F.
11
1990
Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution. Zbl 1168.30025
Peña, Dixan Peña; Sommen, Frank
11
2009
Explicit solutions of the inhomogeneous Dirac equation. Zbl 0883.30041
Sommen, Frank; Jancewicz, Bernard
11
1997
The generalized Clifford-Hermite continuous wavelet transform. Zbl 1221.42058
Brackx, F.; Sommen, Frank
11
2001
The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis. Zbl 1255.30050
De Ridder, Hilde; De Schepper, Hennie; Sommen, Frank
11
2011
Orthosymplectically invariant functions in superspace. Zbl 1312.46065
Coulembier, K.; De Bie, H.; Sommen, F.
11
2010
Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics. Zbl 1273.30040
De Schepper, N.; Sommen, F.
11
2013
Spherical monogenics on the Lie sphere. Zbl 0789.22021
Sommen, F.
10
1990
An extension of the Radon transform to Clifford analysis. Zbl 0628.30046
Sommen, F.
10
1987
Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces. Zbl 1180.30052
Blaya, Ricardo Abreu; Reyes, Juan Bory; Brackx, Fred; De Knock, Bram; De Schepper, Hennie; Peña, Dixan Peña; Sommen, Frank
10
2008
Discrete Clifford analysis: an overview. Zbl 1171.30020
Brackx, Fred; de Schepper, Hennie; Sommen, Frank; van de Voorde, Liesbet
10
2009
Fischer decompositions in superspace. Zbl 1168.58004
De Bie, H.; Sommen, F.
10
2008
A boundary value problem for Hermitian monogenic functions. Zbl 1154.30036
Abreu Blaya, Ricardo; Bory Reyes, Juan; Peña Peña, Dixan; Sommen, Frank
10
2008
Plane wave decompositions of monogenic functions. Zbl 0673.30038
Sommen, F.
10
1988
The Clifford-Gegenbauer polynomials and the associated continuous wavelet transform. Zbl 1062.30057
Brackx, Fred; de Schepper, Nele; Sommen, Frank
10
2004
Orthogonality of Hermite polynomials in superspace and Mehler type formulae. Zbl 1233.33004
Coulembier, Kevin; De Bie, Hendrik; Sommen, Frank
10
2011
On solutions of a discretized heat equation in discrete Clifford analysis. Zbl 1283.39002
Baaske, F.; Bernstein, S.; De Ridder, H.; Sommen, F.
10
2014
The Dirac complex on abstract vector variables: megaforms. Zbl 1078.30044
Sabadini, Irene; Sommen, Frank; Struppa, Daniele C.
10
2003
Phase derivative of monogenic signals in higher dimensional spaces. Zbl 1275.30027
Yang, Yan; Qian, Tao; Sommen, Frank
10
2012
Fueter’s theorem: the saga continues. Zbl 1183.30056
Peña, Dixan Peña; Sommen, Frank
9
2010
The inverse Radon transform and the fundamental solution of the hyperbolic Dirac equation. Zbl 1058.30044
Eelbode, D.; Sommen, F.
9
2004
Riemann-Hilbert problems for monogenic functions in axially symmetric domains. Zbl 1332.30079
He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
9
2016
Taylor series expansion in discrete Clifford analysis. Zbl 1292.30021
De Ridder, Hilde; De Schepper, Hennie; Sommen, Frank
9
2014
Riemann-Hilbert problems for null-solutions to iterated generalized Cauchy-Riemann equations in axially symmetric domains. Zbl 1443.30018
He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
9
2016
An extension of Clifford analysis towards super-symmetry. Zbl 0967.30029
Sommen, Frank
8
2000
Plane waves, biregular functions and hypercomplex Fourier analysis. Zbl 0597.30059
Sommen, F.
8
1985
Hermite and Gegenbauer polynomials in superspace using Clifford analysis. Zbl 1152.30052
De Bie, H.; Sommen, F.
8
2007
Hermitean Clifford-Hermite polynomials. Zbl 1134.30039
Brackx, F.; De Schepper, H.; De Schepper, N.; Sommen, F.
8
2007
A Cauchy integral formula in superspace. Zbl 1179.30054
De Bie, H.; Sommen, F.
8
2009
Martinelli-Bochner type formulae in complex Clifford analysis. Zbl 0651.30027
Sommen, F.
8
1987
On the Szegő-Radon projection of monogenic functions. Zbl 1338.44003
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
8
2016
Higher order Borel-Pompeiu representations in Clifford analysis. Zbl 1355.30044
Bory Reyes, Juan; De Schepper, Hennie; Adán, Alí Guzmán; Sommen, Frank
8
2016
The Clifford-Laguerre continuous wavelet transform. Zbl 1077.42026
Brackx, Fred; De Schepper, Nele; Sommen, Frank
7
2004
Radon and X-ray transforms in Clifford analysis. Zbl 0649.44004
Sommen, Franciscus
7
1989
The spin group in superspace. Zbl 1462.30094
De Schepper, Hennie; Guzmán Adán, Alí; Sommen, Frank
2
2021
Pizzetti and Cauchy formulae for higher dimensional surfaces: a distributional approach. Zbl 1442.58008
Guzmán Adán, Alí; Sommen, Frank
1
2020
Radon-type transforms for holomorphic functions in the Lie ball. Zbl 1421.30065
Sabadini, Irene; Sommen, Franciscus
4
2019
Hypermonogenic solutions and plane waves of the Dirac operator in \(\mathbb{R}^p \times \mathbb{R}^q\). Zbl 1428.30051
Adán, Alí Guzmán; Orelma, Heikki; Sommen, Franciscus
1
2019
Hypermonogenic plane wave solutions of the Dirac equation in superspace. Zbl 1427.30072
Adán, Alí Guzmán; Orelma, Heikki; Sommen, Frank
1
2019
Spin actions in Euclidean and Hermitian Clifford analysis in superspace. Zbl 1375.30072
De Schepper, Hennie; Guzmán Adán, Alí; Sommen, Frank
7
2018
Distributions and integration in superspace. Zbl 1397.58003
Guzmán Adán, Alí; Sommen, Franciscus
4
2018
Hermitian Clifford analysis on superspace. Zbl 1394.30034
De Schepper, Hennie; Guzmán Adán, Alí; Sommen, Frank
1
2018
Segal-Bargmann-Fock modules of monogenic functions. Zbl 1377.30043
Peña Peña, Dixan; Sabadini, Irene; Sommen, Franciscus
14
2017
On the Bargmann-Radon transform in the monogenic setting. Zbl 1376.30036
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
6
2017
Fueter’s theorem for monogenic functions in biaxial symmetric domains. Zbl 1383.30016
Peña Peña, Dixan; Sabadini, Irene; Sommen, Franciscus
4
2017
The radial algebra as an abstract framework for orthogonal and Hermitian Clifford analysis. Zbl 1375.30071
De Schepper, Hennie; Adán, Alí Guzmán; Sommen, Frank
3
2017
On two-sided monogenic functions of axial type. Zbl 1376.30038
Peña, Dixan Peña; Sabadini, Irene; Sommen, Frank
2
2017
On the radial derivative of the delta distribution. Zbl 1380.46032
Brackx, Fred; Sommen, Frank; Vindas, Jasson
1
2017
A Cauchy kernel for the Hermitian submonogenic system. Zbl 1406.30016
Colombo, Fabrizio; Peña, Dixan Peña; Sommen, Frank
1
2017
On a mixed Fischer decomposition in Clifford analysis. Zbl 1364.30055
Bory Reyes, Juan; De Schepper, Hennie; Guzmán Adán, Alí; Sommen, Frank
1
2017
Riemann-Hilbert problems for monogenic functions in axially symmetric domains. Zbl 1332.30079
He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
9
2016
Riemann-Hilbert problems for null-solutions to iterated generalized Cauchy-Riemann equations in axially symmetric domains. Zbl 1443.30018
He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
9
2016
On the Szegő-Radon projection of monogenic functions. Zbl 1338.44003
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
8
2016
Higher order Borel-Pompeiu representations in Clifford analysis. Zbl 1355.30044
Bory Reyes, Juan; De Schepper, Hennie; Adán, Alí Guzmán; Sommen, Frank
8
2016
Reproducing kernels for polynomial null-solutions of Dirac operators. Zbl 1354.30044
De Bie, H.; Sommen, F.; Wutzig, M.
7
2016
Vekua systems in hyperbolic harmonic analysis. Zbl 1332.30076
Eriksson, Sirkka-Liisa; Orelma, Heikki; Sommen, Frank
5
2016
A Fourier-Borel transform for monogenic functionals. Zbl 1406.30018
Sabadini, Irene; Sommen, Franciscus
4
2016
Rotations in discrete Clifford analysis. Zbl 1410.39035
De Ridder, H.; Raeymaekers, T.; Sommen, F.
2
2016
Modern trends in hypercomplex analysis. Selected papers presented at the session on Clifford and quaternionic analysis at the 10th international ISAAC congress, University of Macau, China, August 3–8, 2015. Zbl 1359.30003
1
2016
Differential forms and Clifford analysis. Zbl 1388.30079
Sabadini, Irene; Sommen, Franciscus
1
2016
Introductory Clifford analysis. Zbl 1330.30008
Sommen, Frank; De Schepper, Hennie
3
2015
Boundary value problems on fractal hypersurfaces for the quaternionic Hermitian system in \(\mathbb R^{4n}\). Zbl 1317.30072
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Moreno-García, Tania; Sommen, Frank
2
2015
Hermitian Clifford analysis. Zbl 1330.30006
Sabadini, Irene; Sommen, Frank
2
2015
Biaxial monogenic functions from Funk-Hecke’s formula combined with Fueter’s theorem. Zbl 1326.33017
Peña Peña, Dixan; Sommen, Frank
1
2015
Discrete Hardy spaces. Zbl 1308.44002
Cerejeiras, Paula; Kähler, Uwe; Ku, Min; Sommen, Frank
13
2014
Twisted plane wave expansions using hypercomplex methods. Zbl 1288.30051
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus; Struppa, Daniele C.
12
2014
On solutions of a discretized heat equation in discrete Clifford analysis. Zbl 1283.39002
Baaske, F.; Bernstein, S.; De Ridder, H.; Sommen, F.
10
2014
Taylor series expansion in discrete Clifford analysis. Zbl 1292.30021
De Ridder, Hilde; De Schepper, Hennie; Sommen, Frank
9
2014
A new integral formula for the inverse Fueter mapping theorem. Zbl 1305.30024
Colombo, Fabrizio; Peña Peña, Dixan; Sabadini, Irene; Sommen, Frank
6
2014
The Fueter primitive of biaxially monogenic functions. Zbl 1277.30036
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
5
2014
Distributions and the global operator of slice monogenic functions. Zbl 1306.30019
Colombo, Fabrizio; Sommen, Franciscus
4
2014
Generating functions of orthogonal polynomials in higher dimensions. Zbl 1293.42027
De Bie, Hendrik; Peña Peña, Dixan; Sommen, Frank
3
2014
Dirichlet type problems in Hermitian Clifford analysis. Zbl 1332.30072
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Moreno-García, Tania; Sommen, Frank
2
2014
Sato’s hyperfunctions and boundary values of monogenic functions. Zbl 1325.46045
Sabadini, Irene; Sommen, Franciscus; Struppa, Daniele C.
2
2014
Special functions and systems in Hermitian Clifford analysis: higher codimension. Zbl 1317.30076
De Schepper, Nele; Peña, Dixan Peña; Sommen, Frank
2
2014
Holomorphic approximation of \(L_2\)-functions on the unit sphere in \(\mathbb R^3\). Zbl 1312.30063
De Schepper, Nele; Qian, Tao; Sommen, Frank; Wang, Jinxun
1
2014
Hypercomplex analysis: new perspectives and applications. Selected papers presented at the session on Clifford and quaternionic analysis at the 9th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Krakow, Poland, August 5–9, 2013. Zbl 1300.30002
1
2014
The inverse Fueter mapping theorem in integral form using spherical monogenics. Zbl 1341.30042
Colombo, Fabrizio; Sabadini, Irene; Sommen, Franciscus
14
2013
Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics. Zbl 1273.30040
De Schepper, N.; Sommen, F.
11
2013
Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis. Zbl 1318.30073
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
5
2013
Complex boosts: a Hermitian Clifford algebra approach. Zbl 1269.15021
Ferreira, Milton; Sommen, Frank
4
2013
Special functions and systems in Hermitian Clifford analysis. Zbl 1323.30068
De Schepper, Nele; Peña, Dixan Peña; Sommen, Frank
3
2013
Advances in hypercomplex analysis. Based on the INdAM workshop on different notions of regularity for functions of a quaternionic variable, Rome, Italy, September 13–17, 2010. Zbl 1253.30004
1
2013
Cauchy integral formulae in quaternionic Hermitean Clifford analysis. Zbl 1275.30017
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
16
2012
Fueter polynomials in discrete Clifford analysis. Zbl 1258.30024
De Ridder, H.; De Schepper, H.; Sommen, F.
12
2012
Boundary value problems associated to a Hermitian Helmholtz equation. Zbl 1269.30050
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
11
2012
Phase derivative of monogenic signals in higher dimensional spaces. Zbl 1275.30027
Yang, Yan; Qian, Tao; Sommen, Frank
10
2012
Vekua-type systems related to two-sided monogenic functions. Zbl 1275.30024
Peña, Dixan Peña; Sommen, Frank
6
2012
Boundary value problems for the quaternionic Hermitian system in \(\mathbb R^{4n}\). Zbl 1276.30058
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
5
2012
Discrete Clifford analysis: the one-dimensional setting. Zbl 1262.30051
De Bie, H.; De Ridder, H.; Sommen, F.
4
2012
Cauchy-Kowalevski extensions and monogenic plane waves in Clifford analysis. Zbl 1264.30039
Schepper, Nele De; Sommen, Frank
4
2012
Duality for Hermitean systems in \(\mathbb R^{2n}\). Zbl 1275.30018
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Delanghe, Richard; Sommen, Frank
3
2012
A Hilbert transform for matrix functions on fractal domains. Zbl 1275.30016
Abreu-Blaya, R.; Bory-Reyes, J.; Brackx, F.; De Schepper, H.; Sommen, F.
3
2012
Closed form of the Fourier-Borel kernel in the framework of Clifford analysis. Zbl 1264.30041
de Schepper, N.; Sommen, F.
2
2012
Hölder norm estimate for a Hilbert transform in Hermitean Clifford analysis. Zbl 1256.30046
Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie; Sommen, Frank
1
2012
The inverse Fueter mapping theorem. Zbl 1258.30022
Colombo, Fabrizio; Sabadini, Irene; Sommen, Frank
25
2011
The class of Clifford-Fourier transforms. Zbl 1237.30017
De Bie, Hendrik; De Schepper, Nele; Sommen, Frank
17
2011
A Cauchy-Kowalevski theorem for inframonogenic functions. Zbl 1235.30031
Malonek, Helmuth R.; Peña Peña, Dixan; Sommen, Frank
14
2011
The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis. Zbl 1255.30050
De Ridder, Hilde; De Schepper, Hennie; Sommen, Frank
11
2011
Orthogonality of Hermite polynomials in superspace and Mehler type formulae. Zbl 1233.33004
Coulembier, Kevin; De Bie, Hendrik; Sommen, Frank
10
2011
Hypercomplex analysis and applications. Selected papers presented at the session ‘Clifford and quaternionic analysis’ of the 7th ISAAC conference, London, UK, July 2009. Zbl 1205.30003
1
2011
A differential form approach to Dirac operators on surfaces. Zbl 1235.30032
Orelma, Heikki; Sommen, Frank
1
2011
A holomorphic extension theorem using Clifford analysis. Zbl 1222.30041
Abreu Blaya, Ricardo; Bory Reyes, Juan; Peña Peña, Dixan; Sommen, Frank
1
2011
The Fueter mapping theorem in integral form and the \(\mathcal F\)-functional calculus. Zbl 1225.47019
Colombo, Fabrizio; Sabadini, Irene; Sommen, Frank
45
2010
Discrete function theory based on skew Weyl relations. Zbl 1201.30062
De Ridder, Hilde; De Schepper, Hennie; Kähler, Uwe; Sommen, Frank
24
2010
Fischer decomposition by inframonogenic functions. Zbl 1217.30047
Malonek, Helmuth R.; Peña Peña, Dixan; Sommen, Frank
18
2010
Orthosymplectically invariant functions in superspace. Zbl 1312.46065
Coulembier, K.; De Bie, H.; Sommen, F.
11
2010
Fueter’s theorem: the saga continues. Zbl 1183.30056
Peña, Dixan Peña; Sommen, Frank
9
2010
A Hermitian Cauchy formula on a domain with fractal boundary. Zbl 1201.30060
Abreu-Blaya, R.; Bory-Reyes, J.; Brackx, F.; De Schepper, H.; Sommen, F.
7
2010
The Clifford-Fourier integral kernel in even dimensional Euclidean space. Zbl 1208.42003
Brackx, Fred; de Schepper, Nele; Sommen, Frank
6
2010
\(q\)-deformed harmonic and Clifford analysis and the \(q\)-Hermite and Laguerre polynomials. Zbl 1193.81054
Coulembier, K.; Sommen, F.
5
2010
A note on the Fueter theorem. Zbl 1207.30075
Peña Peña, Dixan; Sommen, Frank
5
2010
Holomorphic extension theorems in Lipschitz domains of \({\mathbb{C}}^{2}\). Zbl 1193.30068
Blaya, Ricardo Abreu; Reyes, Juan Bory; Peña, Dixan Peña; Sommen, Frank
3
2010
The cylindrical Fourier transform. Zbl 1211.65177
Brackx, Fred; De Schepper, Nele; Sommen, Frank
3
2010
Biregular extendability via isotonic Clifford analysis. Zbl 1195.30067
Abreu Blaya, Ricardo; Bory Reyes, Juan; Peña Peña, Dixan; Sommen, Frank
1
2010
On Cauchy and Martinelli-Bochner integral formulae in Hermitean Clifford analysis. Zbl 1182.30081
Brackx, F.; De Knock, B.; De Schepper, H.; Sommen, F.
29
2009
Spherical harmonics and integration in superspace: II. Zbl 1179.30053
De Bie, H.; Eelbode, D.; Sommen, F.
18
2009
Integration in superspace using distribution theory. Zbl 1187.58011
Coulembier, K.; de Bie, H.; Sommen, F.
16
2009
Discrete Clifford analysis: a germ of function theory. Zbl 1173.30034
Brackx, F.; De Schepper, H.; Sommen, F.; Van de Voorde, L.
15
2009
A basic framework for discrete Clifford analysis. Zbl 1186.30044
de Schepper, Hennie; Sommen, Frank; van de Voorde, Liesbet
14
2009
Monogenic Gaussian distribution in closed form and the Gaussian fundamental solution. Zbl 1168.30025
Peña, Dixan Peña; Sommen, Frank
11
2009
Discrete Clifford analysis: an overview. Zbl 1171.30020
Brackx, Fred; de Schepper, Hennie; Sommen, Frank; van de Voorde, Liesbet
10
2009
A Cauchy integral formula in superspace. Zbl 1179.30054
De Bie, H.; Sommen, F.
8
2009
Generalized hermitian Clifford-Hermite polynomials and the associated wavelet transform. Zbl 1169.30023
Brackx, Fred; de Schepper, Hennie; de Schepper, Nele; Sommen, Frank
4
2009
Hypercomplex analysis. Selected papers of the 6th ISAAC conference, Ankara, Turkey, August 13–18, 2007. Zbl 1159.30003
3
2009
On the CK-extension for a special overdetermined system in complex Clifford analysis. Zbl 1168.30327
De Knock, Bram; Peña, Dixan Peña; Sommen, Frank
2
2009
Criteria for monogenicity of Clifford-algebra-valued functions. Zbl 1180.30051
Abreu Blaya, Ricardo; Reyes, Juan Bory; Peña Peña, Dixan; Sommen, Frank
2
2009
Clifford algebra applied to the heat equation. Zbl 1185.30051
Cerejeiras, P.; Sommen, F.
1
2009
The Hermitian Clifford analysis toolbox. Zbl 1177.30064
Brackx, Fred; De Schepper, Hennie; Sommen, Frank
53
2008
Fundamental solutions for the super Laplace and Dirac operators and all their natural powers. Zbl 1143.30022
De Bie, H.; Sommen, F.
12
2008
Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces. Zbl 1180.30052
Blaya, Ricardo Abreu; Reyes, Juan Bory; Brackx, Fred; De Knock, Bram; De Schepper, Hennie; Peña, Dixan Peña; Sommen, Frank
10
2008
Fischer decompositions in superspace. Zbl 1168.58004
De Bie, H.; Sommen, F.
10
2008
A boundary value problem for Hermitian monogenic functions. Zbl 1154.30036
Abreu Blaya, Ricardo; Bory Reyes, Juan; Peña Peña, Dixan; Sommen, Frank
10
2008
The cylindrical Fourier spectrum of an \(L_2\)-basis consisting of generalized Clifford-Hermite functions. Zbl 1163.65339
Brackx, F.; De Schepper, N.; Sommen, F.
4
2008
...and 141 more Documents
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Cited by 693 Authors

130 Sommen, Franciscus
84 Sabadini, Irene
68 Brackx, Fred F.
66 Colombo, Fabrizio
64 Abreu-Blaya, Ricardo
61 De Schepper, Hennie
59 Bory Reyes, Juan
46 Eelbode, David
42 De Bie, Hendrik
40 Kraußhar, Rolf Sören
40 Qian, Tao
34 Kähler, Uwe
33 Struppa, Daniele Carlo
32 Soucek, Vladimir
29 Alpay, Daniel Aron
27 Cerejeiras, Paula
27 Constales, Denis
25 Peña Peña, Dixan
24 Lávička, Roman
24 Ren, Guangbin
23 Vieira, Nelson
20 Ku, Min
18 Wang, Wei
16 Adán, Alí Guzmán
16 Delanghe, Richard
16 Shapiro, Michael V.
15 Bernstein, Swanhild
15 Li, Pingrun
15 Raeymaekers, Tim
13 Diki, Kamal
13 Gentili, Graziano
13 Qiao, Yuying
13 Yuan, Hongfen
12 Ferreira, Milton
12 Gürlebeck, Klaus
12 He, Fuli
12 Malonek, Helmuth Robert
11 Dang, Pei
11 De Ridder, Hilde
11 Dinh, Doan Cong
11 Gu, Longfei
11 Orelma, Heikki
11 Van Lancker, Peter
11 Yang, Heju
10 Damiano, Alberto
10 De Knock, Bram
10 Kou, Kit-Ian
10 Lian, Pan
10 Luna-Elizarrarás, María Elena
10 Moreno García, Tania
10 Perotti, Alessandro
10 Yang, Yan
9 Cação, Isabel
9 De Martino, Antonino
9 Ding, Chao
9 Hitzer, Eckhard
9 Morais, João Pedro
9 Vanegas, Judith C.
8 De Schepper, Nele
8 Falcão, Maria Irene
8 Grob, Dennis
8 Moreno García, Arsenio
8 Pinton, Stefano
8 Rodrigues, Maria Manuela
8 Wang, Haiyan
7 Bahri, Mawardi
7 Du, Jinyuan
7 Faustino, Nelson José Rodrigues
7 Gantner, Jonathan
7 Li, Xingmin
7 Stoppato, Caterina
7 Vâjiac, Adrian I.
7 Vajiac, Mihaela B.
7 Zhao, Jiman
6 Ben Mabrouk, Anouar
6 Bureš, Jarolím
6 Coulembier, Kevin
6 de Almeida, Regina
6 Fei, Minggang
6 Ghiloni, Riccardo
6 González-Cervantes, José Óscar
6 Kisil, Vladimir V.
6 Li, Zunfeng
6 Peng, Lizhong
6 Sigarreta Almira, José María
5 Bock, Sebastian
5 Di Teodoro, Antonio Nicola
5 Eriksson, Sirkka-Liisa
5 Kimsey, David Patrick
5 Li, Shanshan
5 Mai, Weixiong
5 Mejjaoli, Hatem
5 Roels, Matthias
5 Salač, Tomáš
5 Santiesteban, Daniel Alfonso
5 Sprößig, Wolfgang
5 Vargas, Franklin
5 Walter, Raymond
5 Wang, Jinxun
5 Wang, Liping
...and 593 more Authors
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Cited in 181 Serials

213 Advances in Applied Clifford Algebras
84 Complex Analysis and Operator Theory
60 Mathematical Methods in the Applied Sciences
59 Journal of Mathematical Analysis and Applications
51 Complex Variables and Elliptic Equations
24 Journal of Geometry and Physics
22 Journal of Mathematical Physics
17 Applied Mathematics and Computation
16 The Journal of Geometric Analysis
15 Zeitschrift für Analysis und ihre Anwendungen
15 Computational Methods and Function Theory
14 Annali di Matematica Pura ed Applicata. Serie Quarta
14 Journal of Functional Analysis
14 Results in Mathematics
14 Boundary Value Problems
12 Transactions of the American Mathematical Society
11 Advances in Mathematics
11 Integral Transforms and Special Functions
10 Mathematische Nachrichten
10 The Journal of Fourier Analysis and Applications
9 Annals of Global Analysis and Geometry
9 Acta Mathematica Sinica. English Series
8 Proceedings of the American Mathematical Society
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Analysis and Mathematical Physics
7 Applicable Analysis
7 Israel Journal of Mathematics
7 Journal of Mathematical Sciences (New York)
7 Journal of Inequalities and Applications
7 Bulletin of the Brazilian Mathematical Society. New Series
7 Science China. Mathematics
6 Abstract and Applied Analysis
6 Mediterranean Journal of Mathematics
5 Czechoslovak Mathematical Journal
5 Chinese Annals of Mathematics. Series B
5 Journal of Difference Equations and Applications
4 Integral Equations and Operator Theory
4 Journal of Approximation Theory
4 Rendiconti del Circolo Matemàtico di Palermo. Serie II
4 Acta Applicandae Mathematicae
4 Revista Matemática Iberoamericana
4 Linear Algebra and its Applications
4 Potential Analysis
4 Applied and Computational Harmonic Analysis
4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
4 Journal of Physics A: Mathematical and Theoretical
3 Communications in Mathematical Physics
3 Linear and Multilinear Algebra
3 Rocky Mountain Journal of Mathematics
3 Archiv der Mathematik
3 Journal of Algebra
3 Journal of Computational and Applied Mathematics
3 Journal of Differential Equations
3 Journal of Number Theory
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 Science in China. Series A
3 Journal of Mathematical Imaging and Vision
3 Journal of Lie Theory
3 Bulletin des Sciences Mathématiques
3 Mathematical Physics, Analysis and Geometry
3 Journal of the European Mathematical Society (JEMS)
3 Milan Journal of Mathematics
3 International Journal of Wavelets, Multiresolution and Information Processing
3 Frontiers of Mathematics in China
2 Computers & Mathematics with Applications
2 Discrete Applied Mathematics
2 Journal d’Analyse Mathématique
2 Letters in Mathematical Physics
2 Reports on Mathematical Physics
2 Arkiv för Matematik
2 Chaos, Solitons and Fractals
2 International Journal of Mathematics and Mathematical Sciences
2 Mathematische Annalen
2 Mathematische Zeitschrift
2 Memoirs of the American Mathematical Society
2 Michigan Mathematical Journal
2 Publications of the Research Institute for Mathematical Sciences, Kyoto University
2 Tokyo Journal of Mathematics
2 Advances in Applied Mathematics
2 Constructive Approximation
2 Journal of the American Mathematical Society
2 Neural Networks
2 International Journal of Mathematics
2 Differential Geometry and its Applications
2 Experimental Mathematics
2 Fractals
2 Filomat
2 Wuhan University Journal of Natural Sciences (WUJNS)
2 Differential Equations
2 Journal of Evolution Equations
2 Communications on Pure and Applied Analysis
2 Quantum Information Processing
2 Analysis and Applications (Singapore)
2 Oberwolfach Reports
2 Banach Journal of Mathematical Analysis
2 Journal of Pseudo-Differential Operators and Applications
2 Journal of Applied Analysis and Computation
2 Journal of Function Spaces
2 AIMS Mathematics
...and 81 more Serials
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Cited in 56 Fields

759 Functions of a complex variable (30-XX)
171 Linear and multilinear algebra; matrix theory (15-XX)
161 Partial differential equations (35-XX)
143 Harmonic analysis on Euclidean spaces (42-XX)
102 Operator theory (47-XX)
86 Several complex variables and analytic spaces (32-XX)
72 Global analysis, analysis on manifolds (58-XX)
71 Functional analysis (46-XX)
66 Quantum theory (81-XX)
58 Integral transforms, operational calculus (44-XX)
52 Special functions (33-XX)
50 Differential geometry (53-XX)
43 Potential theory (31-XX)
34 Number theory (11-XX)
34 Information and communication theory, circuits (94-XX)
33 Nonassociative rings and algebras (17-XX)
30 Topological groups, Lie groups (22-XX)
30 Abstract harmonic analysis (43-XX)
26 Integral equations (45-XX)
24 Difference and functional equations (39-XX)
24 Numerical analysis (65-XX)
19 Real functions (26-XX)
15 Ordinary differential equations (34-XX)
15 Relativity and gravitational theory (83-XX)
13 Approximations and expansions (41-XX)
12 Combinatorics (05-XX)
12 Group theory and generalizations (20-XX)
9 Dynamical systems and ergodic theory (37-XX)
9 Geometry (51-XX)
8 Measure and integration (28-XX)
8 Probability theory and stochastic processes (60-XX)
8 Computer science (68-XX)
8 Fluid mechanics (76-XX)
8 Optics, electromagnetic theory (78-XX)
7 Algebraic geometry (14-XX)
7 Associative rings and algebras (16-XX)
7 Biology and other natural sciences (92-XX)
6 Mechanics of particles and systems (70-XX)
5 Commutative algebra (13-XX)
4 Field theory and polynomials (12-XX)
4 Statistics (62-XX)
3 Category theory; homological algebra (18-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
3 General topology (54-XX)
3 Algebraic topology (55-XX)
3 Manifolds and cell complexes (57-XX)
3 Mechanics of deformable solids (74-XX)
3 Systems theory; control (93-XX)
2 General and overarching topics; collections (00-XX)
2 Convex and discrete geometry (52-XX)
2 Geophysics (86-XX)
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1 Statistical mechanics, structure of matter (82-XX)
1 Astronomy and astrophysics (85-XX)
1 Operations research, mathematical programming (90-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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