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Complex Variables, Theory and Application: An International Journal Volume 39, 1999 - Issue 3
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Original Articles

A hypercomplex derivative of monogenic functsions in and its Applications

K. Gürlebeck Technische Universitat Chemnitz, Fakultät für Mathematik, Chemnitz, D-09107, Germany
&
Helmuth R. Malonek Departamento de Matemática, Universidade de Aveiro, Aveiro, Potugal, P-3810
Pages 199-228 | Received 10 Mar 1998, Published online: 29 May 2007

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Gamal Hassan & Mohra Zayed. (2023) Approximation of monogenic functions by hypercomplex Ruscheweyh derivative bases. Complex Variables and Elliptic Equations 68:12, pages 2073-2092.
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Sebastian Bock. (2019) A generalized monogenic exponential function in ℍ. Complex Variables and Elliptic Equations 64:11, pages 1881-1897.
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S. Bock. (2012) On a three dimensional analogue to the holomorphic z-powers: power series and recurrence formulae. Complex Variables and Elliptic Equations 57:12, pages 1349-1370.
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S. Bock. (2012) On a three-dimensional analogue to the holomorphic z-powers: Laurent series expansions. Complex Variables and Elliptic Equations 57:12, pages 1271-1287.
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J. Morais & K. Gürlebeck. (2012) Real-part estimates for solutions of the Riesz system in ℝ3 . Complex Variables and Elliptic Equations 57:5, pages 505-522.
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I. Cação & K. Gürlebeck. (2007) On monogenic primitives of monogenic functions. Complex Variables and Elliptic Equations 52:10-11, pages 1081-1100.
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I. Cação, K. Gürlebeck & S. Bock. (2006) On derivatives of spherical monogenics. Complex Variables and Elliptic Equations 51:8-11, pages 847-869.
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R. Delanghe. (2006) On primitives of monogenic functions. Complex Variables and Elliptic Equations 51:8-11, pages 959-970.
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Doan Cong Dinh. (2022) Somigliana formula in quaternion analysis. Mechanics Research Communications 126, pages 104018.
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Isabel Cação, M. Irene Falcão, Helmuth R. Malonek & Graça Tomaz. (2021) A Sturm‐Liouville equation on the crossroads of continuous and discrete hypercomplex analysis. Mathematical Methods in the Applied Sciences.
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Manuel Fernandez‐Guasti. (2019) Components exponential scator holomorphic function. Mathematical Methods in the Applied Sciences 43:3, pages 1017-1034.
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Joaõ Morais. 2019. Topics in Clifford Analysis. Topics in Clifford Analysis 251 266 .
Karen Avetisyan & Klaus Gürlebeck. (2018) On weighted Dirichlet spaces of monogenic functions in. Mathematical Methods in the Applied Sciences 41:18, pages 9511-9528.
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Mohamed Abdalla, Mahmoud Abul‐Ez & João Morais. (2018) On the construction of generalized monogenic Bessel polynomials. Mathematical Methods in the Applied Sciences 41:18, pages 9335-9348.
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Chao Ding, Sebastian Bock & Klaus Gürlebeck. (2018) Special bases for solutions of a generalized Maxwell system in 3‐dimensional space. Mathematical Methods in the Applied Sciences 41:13, pages 5308-5326.
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M. Fernández‐Guasti. (2018) Differential quotients in elliptic scator algebra. Mathematical Methods in the Applied Sciences 41:12, pages 4827-4840.
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Sebastian Bock. On generalized Kolosov-Muskhelishvili formulae for the finite cylinder. On generalized Kolosov-Muskhelishvili formulae for the finite cylinder.
Lidia Aceto, Helmut Robert Malonek & Graça Tomaz. (2017) Matrix approach to hypercomplex Appell polynomials. Applied Numerical Mathematics 116, pages 2-9.
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Sirkka-Liisa Eriksson & Heikki Orelma. (2016) Quaternionic k-Hyperbolic Derivative. Complex Analysis and Operator Theory 11:5, pages 1193-1204.
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Ricardo Abreu Blaya, Juan Bory Reyes, Alí Guzmán Adán & Uwe Kähler. (2016) On the $$\varphi $$ φ -Hyperderivative of the $$\psi $$ ψ -Cauchy-Type Integral in Clifford Analysis. Computational Methods and Function Theory 17:1, pages 101-119.
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I. Cação, M. I. Falcão & H. R. Malonek. (2015) Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials. Advances in Applied Clifford Algebras 27:1, pages 71-85.
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Isabel Cação, Helmuth R. Malonek & Graça Tomaz. 2017. Computational Science and Its Applications – ICCSA 2017. Computational Science and Its Applications – ICCSA 2017 409 421 .
J. Morais, H. M. Nguyen & K. I. Kou. (2016) On 3D orthogonal prolate spheroidal monogenics. Mathematical Methods in the Applied Sciences 39:4, pages 635-648.
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S. Bock, K. Gürlebeck, D. Legatiuk & H. M. Nguyen. (2015) ψ ‐Hyperholomorphic functions and a Kolosov–Muskhelishvili formula . Mathematical Methods in the Applied Sciences 38:18, pages 5114-5123.
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J. Morais, K. I. Kou & H. T. Le. (2015) Generalized holomorphic orthogonal function systems over infinite cylinders. Mathematical Methods in the Applied Sciences 38:12, pages 2574-2588.
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G.F. Hassan & L. Aloui. (2014) Bernoulli and Euler Polynomials in Clifford Analysis. Advances in Applied Clifford Algebras 25:2, pages 351-376.
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J. Morais & C.A. Nolder. (2014) Local distortion of M-conformal mappings. Applied Mathematics and Computation 249, pages 554-568.
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Sebastian Bock. (2014) On Monogenic Series Expansions with Applications to Linear Elasticity. Advances in Applied Clifford Algebras 24:4, pages 931-943.
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Carla Cruz, Maria Irene Falcão & Helmuth R. Malonek. (2014) Monogenic pseudo-complex power functions and their applications. Mathematical Methods in the Applied Sciences 37:12, pages 1723-1735.
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Carla Cruz, M. Irene Falcão & Helmuth R. Malonek. 2014. Computational Science and Its Applications – ICCSA 2014. Computational Science and Its Applications – ICCSA 2014 204 220 .
Klaus Gürlebeck, Hung Manh Nguyen & Dmitrii Legatiuk. 2014. Computational Science and Its Applications – ICCSA 2014. Computational Science and Its Applications – ICCSA 2014 189 203 .
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J. Morais, K. Avetisyan & K. Gürlebeck. (2013) On Riesz systems of harmonic conjugates in. Mathematical Methods in the Applied Sciences 36:12, pages 1598-1614.
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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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J. Morais & M. Ferreira. (2013) 3D deformations by means of monogenic functions. Mathematical Methods in the Applied Sciences 36:7, pages 780-793.
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Carla Cruz, M. Irene Falcão & Helmuth R. Malonek. 2013. Computational Science and Its Applications – ICCSA 2013. Computational Science and Its Applications – ICCSA 2013 293 303 .
João Pedro Morais & Klaus Gürlebeck. (2012) Bloch’s Theorem in the Context of Quaternion Analysis. Computational Methods and Function Theory 12:2, pages 541-558.
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Mohra Zayed, Mahmoud Abul-Ez & João Pedro Morais. (2012) Generalized Derivative and Primitive of Cliffordian Bases of Polynomials Constructed Through Appell Monomials. Computational Methods and Function Theory 12:2, pages 501-515.
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Isabel Cação, Maria Irene Falcão & Helmuth R. Malonek. (2012) Matrix Representations of a Special Polynomial Sequence in Arbitrary Dimension. Computational Methods and Function Theory 12:2, pages 371-391.
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H. R. Malonek & M. I. Falcão. (2012) On Paravector Valued Homogeneous Monogenic Polynomials with Binomial Expansion. Advances in Applied Clifford Algebras 22:3, pages 789-801.
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Richard Delanghe, Roman Lávička & Vladimír Souček. (2012) The Gelfand–Tsetlin bases for Hodge–de Rham systems in Euclidean spaces. Mathematical Methods in the Applied Sciences 35:7, pages 745-757.
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Vladimír Souček, Richard Delanghe & Roman Lávička. (2011) The Fischer decomposition for Hodge‐de Rham systems in Euclidean spaces. Mathematical Methods in the Applied Sciences 35:1, pages 10-16.
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M. Elena Luna-Elizarrarás, Marco A. Macías-Cedeño & Michael Shapiro. 2012. Recent Progress in Operator Theory and Its Applications. Recent Progress in Operator Theory and Its Applications 179 195 .
M. E. Luna-Elizarrarás & M. Shapiro. (2011) A Survey on the (Hyper-) Derivatives in Complex, Quaternionic and Clifford Analysis. Milan Journal of Mathematics 79:2, pages 521-542.
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J. Morais, H. T. Le & W. Sprößig. (2011) On some constructive aspects of monogenic function theory in ℝ 4 . Mathematical Methods in the Applied Sciences 34:14, pages 1694-1706.
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J. Morais & H. T. Le. (2011) Orthogonal Appell systems of monogenic functions in the cylinder. Mathematical Methods in the Applied Sciences 34:12, pages 1472-1486.
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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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Jinyuan Du & Na Xu. (2010) On Boundary Behavior of the Cauchy Type Integrals with Values in a Universal Clifford Algebra. Advances in Applied Clifford Algebras 21:1, pages 49-87.
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K. Gürlebeck & J. Morais. 2011. Recent Advances in Computational and Applied Mathematics. Recent Advances in Computational and Applied Mathematics 143 158 .
Carla Cruz, M. I. Falcão & H. R. Malonek. 2011. Computational Science and Its Applications - ICCSA 2011. Computational Science and Its Applications - ICCSA 2011 358 373 .
I. Cação & H. R. Malonek. 2011. Computational Science and Its Applications - ICCSA 2011. Computational Science and Its Applications - ICCSA 2011 316 326 .
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M. I. Falcão & Fernando Miranda. 2011. Computational Science and Its Applications - ICCSA 2011. Computational Science and Its Applications - ICCSA 2011 200 214 .
Isabel Cação. (2010) Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in ℝ3. Numerical Algorithms 55:2-3, pages 191-203.
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H.R. Malonek & R. De Almeida. (2010) A note on a generalized Joukowski transformation. Applied Mathematics Letters 23:10, pages 1174-1178.
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S. Bock & K. Gürlebeck. (2009) On a generalized Appell system and monogenic power series. Mathematical Methods in the Applied Sciences 33:4, pages 394-411.
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H. R. Malonek & M. I. Falcão. (2009) 3D‐mappings by means of monogenic functions and their approximation. Mathematical Methods in the Applied Sciences 33:4, pages 423-430.
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L. Aloui & G. F. Hassan. (2010) Hypercomplex derivative bases of polynomials in Clifford analysis. Mathematical Methods in the Applied Sciences 33:3, pages 350-357.
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Klaus Gürlebeck & João Pedro Morais. (2009) Bohr Type Theorems for Monogenic Power Series. Computational Methods and Function Theory 9:2, pages 633-651.
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S. Bock & K. Gürlebeck. (2008) On a spatial generalization of the Kolosov–Muskhelishvili formulae. Mathematical Methods in the Applied Sciences 32:2, pages 223-240.
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K. Gürlebeck & H. R. Malonek. (2009) On strict inclusions of weighted dirichlet spaces of monogenic functions. Bulletin of the Australian Mathematical Society 64:1, pages 33-50.
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U. Kähler & A. M. Martins. (2001) Quaternionic Beltrami-type equations and homeomorphic solutions. Advances in Applied Clifford Algebras 11:S2, pages 177-182.
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I. Cação, K. Gürlebeck & H. Malonek. (2001) Special monogenic polynomials andL 2-approximation. Advances in Applied Clifford Algebras 11:S2, pages 47-60.
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J. Cnops, R. Delanghe, K. G?rlebeck & M. V. Shapiro. (2001) Q p -spaces in clifford analysis. Advances in Applied Clifford Algebras 11:S1, pages 201-218.
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Klaus Gürlebeck. 2001. Clifford Analysis and Its Applications. Clifford Analysis and Its Applications 81 89 .
Paula Cerejeiras & Uwe Kähler. 2001. Clifford Analysis and Its Applications. Clifford Analysis and Its Applications 49 58 .
Helmuth R. Malonek. 2001. Clifford Analysis and Its Applications. Clifford Analysis and Its Applications 213 222 .
Vladimir V. Kisil. 2001. Clifford Analysis and Its Applications. Clifford Analysis and Its Applications 135 141 .
H. R. Malonek. 2001. Proceedings of the Second ISAAC Congress. Proceedings of the Second ISAAC Congress 1481 1495 .
Helmuth R. Malonek. 2000. Clifford Algebras and their Applications in Mathematical Physics. Clifford Algebras and their Applications in Mathematical Physics 273 285 .

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