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Applicable Analysis
An International Journal
Volume 12, 1981 - Issue 1
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Original Articles

A product and an exponential function in hypercomplex function theory

F. Sommen Seminar of Higher Analysis, State University of Ghent, Krijgsiaan 271, Gent, B-9000, Belgium
Pages 13-26 | Published online: 02 May 2007

Citations (37)

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Daniel Alpay & H. Turgay Kaptanoğlu. (2012) Quaternionic Hilbert spaces and a von Neumann inequality. Complex Variables and Elliptic Equations 57:6, pages 667-675.
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D. Alpay, F. M. Correa-Romero, M. E. Luna-Elizarrarás & M. Shapiro. (2007) Hyperholomorphic rational functions: the Clifford analysis case. Complex Variables and Elliptic Equations 52:1, pages 59-78.
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John Ryan. (1983) Special functions and relations within complex clifford analysis I. Complex Variables, Theory and Application: An International Journal 2:2, pages 177-198.
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F. Sommen. (1983) Hypercomplex fourier and laplace transforms II. Complex Variables, Theory and Application: An International Journal 1:2-3, pages 209-238.
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F. Sommen. (1982) Some connections between clifford analysis and complex analysis. Complex Variables, Theory and Application: An International Journal 1:1, pages 97-118.
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Articles from other publishers (32)

Tawseef Ahmad Sheikh & Neyaz A. Sheikh. (2023) Short time quadratic-phase quaternionic Fourier transform and associated uncertainty principle. São Paulo Journal of Mathematical Sciences 17:2, pages 1125-1141.
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V. G. Labunets, V. P. Chasovskikh & E. N. Starikov. (2023) New many-parameter Fourier–Clifford transforms. Digital models and solutions 2:3, pages 5-22.
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Valeriy Labunets, Victor Chasovskikh, Evgeniy Starikov & Nicolas Ostheimer. New many-parameter Fourier-Clifford transforms. New many-parameter Fourier-Clifford transforms.
Eckhard Hitzer. 2023. Quaternionic Integral Transforms. Quaternionic Integral Transforms 1 58 .
Robert Reynolds & Allan Stauffer. (2022) Extended Ohtsuka–Vălean Sums. Symmetry 14:8, pages 1551.
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Valeriy Labunets, Victor Chasovskikh & Nicolas Ostheimer. (2021) All Fourier-Clifford Transforms. All Fourier-Clifford Transforms.
Daniel Alpay, Fabrizio Colombo, Kamal Diki & Irene Sabadini. (2021) On a Polyanalytic Approach to Noncommutative de Branges–Rovnyak Spaces and Schur Analysis. Integral Equations and Operator Theory 93:4.
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Daniel Alpay, Ismael L. Paiva & Daniele C. Struppa. (2020) A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics. Israel Journal of Mathematics 236:1, pages 207-246.
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Valeriy G. Labunets & Ekaterina Ostheimer. 2020. Advances in Artificial Systems for Medicine and Education III. Advances in Artificial Systems for Medicine and Education III 76 92 .
V G Labunets & E V Ostheimer. (2019) Intelligent OFDM telecommunication system. Part 2. Examples of complex and quaternion many-parameter transforms. Journal of Physics: Conference Series 1368:5, pages 052022.
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Daniel Alpay, Fabrizio Colombo & Irene Sabadini. (2019) Herglotz functions: The Fueter variables case. Linear Algebra and its Applications 563, pages 75-97.
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Daniel Alpay, María E. Luna-Elizarrarás, Michael Shapiro & Daniele Struppa. (2018) Gleason’s problem, rational functions and spaces of left-regular functions: The split-quaternion setting. Israel Journal of Mathematics 226:1, pages 319-349.
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D. Alpay, P. Cerejeiras & U. Kähler. (2017) Gleason’s problem associated to the fractional Cauchy-Riemann operator, Fueter series, Drury-Arveson space and related topics. Proceedings of the American Mathematical Society 145:11, pages 4821-4835.
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Igor V. Kanatchikov. (2017) On the spectrum of DW Hamiltonian of quantum SU(2) gauge field. International Journal of Geometric Methods in Modern Physics 14:09, pages 1750123.
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Irene SABADINI & Franciscus SOMMEN. (2016) A Fourier–Borel transform for monogenic functionals. Journal of the Mathematical Society of Japan 68:4.
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Daniel Alpay, Fabrizio Colombo & Irene Sabadini. 2015. Operator Theory. Operator Theory 1745 1786 .
Nele De Schepper, Tao Qian, Frank Sommen & Jinxun Wang. (2014) Holomorphic approximation of -functions on the unit sphere in . Journal of Mathematical Analysis and Applications 416:2, pages 659-671.
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Hendrik De Bie, Dixan Peña Peña & Frank Sommen. (2014) Generating functions of orthogonal polynomials in higher dimensions. Journal of Approximation Theory 178, pages 30-40.
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Daniel Alpay, Fabrizio Colombo & Irene M. Sabadini. 2014. Operator Theory. Operator Theory 1 38 .
N. De Schepper & F. Sommen. (2013) Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics. Bulletin of the Brazilian Mathematical Society, New Series 44:2, pages 321-350.
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Dixan Peña Peña. (2012) Shifted Appell Sequences in Clifford Analysis. Results in Mathematics 63:3-4, pages 1145-1157.
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Daniel Alpay, Palle Jorgensen, Ron Seager & Dan Volok. (2012) On discrete analytic functions: Products, rational functions and reproducing kernels. Journal of Applied Mathematics and Computing 41:1-2, pages 393-426.
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Mawardi Bahri. 2013. Quaternion and Clifford Fourier Transforms and Wavelets. Quaternion and Clifford Fourier Transforms and Wavelets 285 298 .
I. Cação, M.I. Falcão & H.R. Malonek. (2011) Laguerre derivative and monogenic Laguerre polynomials: An operational approach. Mathematical and Computer Modelling 53:5-6, pages 1084-1094.
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I. Cação & H. R. Malonek. 2011. Computational Science and Its Applications - ICCSA 2011. Computational Science and Its Applications - ICCSA 2011 316 326 .
Fred Brackx, Nele De Schepper & Frank Sommen. 2009. Advances in IMAGING AND ELECTRON PHYSICS. Advances in IMAGING AND ELECTRON PHYSICS 55 201 .
Daniel Alpay & David Levanony. (2008) Rational Functions Associated with the White Noise Space and Related Topics. Potential Analysis 29:2, pages 195-220.
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Fred Brackx, Nele De Schepper & Frank Sommen. (2006) The Two-Dimensional Clifford-Fourier Transform. Journal of Mathematical Imaging and Vision 26:1-2, pages 5-18.
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G. Laville & I. Ramadanoff. (2006) An integral transform generating elementary functions in Clifford analysis. Mathematical Methods in the Applied Sciences 29:6, pages 637-654.
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Daniel Alpay, Michael Shapiro & Dan Volok. 2006. Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems. Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems 19 45 .
Rafal Ablamowicz, William E. Baylis, Thomas Branson, Pertti Lounesto, Ian Porteous, John Ryan, J. M. Selig & Garret SobczykJohn Ryan. 2004. Lectures on Clifford (Geometric) Algebras and Applications. Lectures on Clifford (Geometric) Algebras and Applications 53 89 .
A.K. Kwaśniewski. (1985) Generalization of Cauchy–Riemann equations. Reports on Mathematical Physics 22:1, pages 133-148.
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