Lehrstuhl A für Mathematik, RWTH Aachen
Analysis und Zahlentheorie
Prof. Dr. A. Krieg
Analysis und Zahlentheorie
Prof. Dr. A. Krieg
(mit D. Constales und D. Grob)
On generalized Helmholtz type equations in concentric annular domains in R3
Erscheint in: Mathematical Methods in the Applied Sciences.
(mit D. Constales)
Multiperiodic eigensolutions to the Dirac operator and applications to the generalized Helmholtz equation on flat cylinders and on the n–torus
Erscheint in: Mathematical Methods in the Applied Sciences.
(mit E. Bulla, D. Constales und J. Ryan)
Dirac Type Operators for Arithmetic Subgroups of Generalized Modular Groups
Erscheint in: Journal für die Reine und Angewandte Mathematik (Crelle's Journal).
(mit D. Constales und R. De Almeida)
Basics of a generalized Wiman–Valiron theory for monogenic Taylor series of finite convergence radius
Erscheint in: Mathematische Zeitschrift.
(mit D. Constales und D. Grob)
Constructing 3D mappings onto the unit sphere with the hypercomplex Szego kernel
Eingereicht zur Veröffentlichung in: Journal of Computational and Applied Mathematics
(mit D. Constales und D. Grob)
Explicit formulas for the Green's function and the Bergman kernel for monogenic functions in annular shaped domains in Rn+1
Eingereicht zur Veröffentlichung in: Revista Matematica Iberoamericana
(mit D. Constales und D. Grob)
Reproducing kernel functions of solutions to polynomial Dirac equations in the annulus of the unit ball in Rn and applications to boundary value problems
Eingereicht zur Veröffentlichung in: Journal of Mathematical Analysis and Applications
(mit D. Constales und R. De Almeida)
A Generalization of Wiman and Valiron's theory to the Clifford analysis setting
Cubo – A Mathematical Journal 11, No. 1, 1–20 (2009).
(mit I. Cação und D. Constales)
Explicit representations of the regular solutions of the time–harmonic Maxwell equations combined with the radial symmetric Euler operator
Mathematical Methods in the Applied Sciences 32, No.1, 1–11 (2009).
(mit I. Cação und D. Constales)
On rotationally symmetric Dirac equations and hypergeometric functions I
Archiv der Mathematik 90, No. 5, 440–449 (2008).
(mit D. Constales und R. de Almeida)
Applications of the maximum term and the central index in the asymptotic growth analysis of entire solutions to higher dimensional polynomial Cauchy–Riemann equations
Complex Variables and Elliptic equations 53, No. 3, 195–213 (2008).
(mit D. Constales)
On the Navier–Stokes equation with Free Convection in three dimensional unbounded triangular channels
Mathematical Methods in the Applied Sciences 31, No. 6, 735–751 (2008).
(mit H. Albuquerque)
Multiplicative invariant lattices in Rn obtained by twisting of group algebra and some explicit characterizations
Journal of Algebra 319, No. 3, 1116–1131 (2008).
(mit S.–L. Eriksson)
Preface (Editorial preface to Selected papers of the conference on function theories in higher dimensions, Tampere, Finland, June 12–16, 2006)
Advances in Applied Clifford Algebras 17, No. 3, 307–309 (2007).
(mit D. Constales und J. Ryan)
k–hypermonogenic automorphic forms
Journal of Number Theory 126, No. 2, 254–271 (2007).
(mit D. Constales und R. de Almeida)
On the growth type of entire monogenic functions
Archiv der Mathematik 88, No. 2, 153–163 (2007).
(mit D. Constales und R. de Almeida)
On the relation between the growth and the Taylor coefficients of entire solutions to the higher dimensional Cauchy–Riemann system in Rn+1
Journal of Mathematical Analysis and its Applications 327, No. 2, 763–775 (2007).
(mit J. Ryan)
Some Conformally Flat Spin Manifolds, Dirac Operators and Automorphic Forms
Journal of Mathematical Analysis and its Applications 325, No. 1, 359–376 (2007).
(mit I. Cação und D. Constales)
On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations
Archiv der Mathematik 87, No. 5, 468–477 (2006).
(mit D. Constales und R. de Almeida)
On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy–Riemann equations
Mathematical Methods in the Applied Sciences 29, No. 14, 1663–1686 (2006).
(mit D. Constales und R. de Almeida)
Further results on the asymptotic growth of entire solutions of iterated Dirac equations in Rn
Mathematical Methods in the Applied Sciences 29, No. 5, 537–556 (2006).
(mit D. Constales)
Bergman Spaces of higher dimensional hyperbolic polyhedron type domains I
Mathematical Methods in the Applied Sciences 29, No. 1, 85–98 (2006).
(mit R. de Almeida)
On the asymptotic growth of entire monogenic functions
Zeitschrift für Analysis und ihre Anwendungen 24, No. 4, 791–813 (2005).
(mit D. Constales)
Hilbert Spaces of Solutions to Polynomial Dirac equations, Fourier Transforms and Reproducing Kernel Functions for Cylindrical Domains
Zeitschrift für Analysis und ihre Anwendungen 24, No. 3, 611–636 (2005).
(mit J. Ryan und Qiao Yuying)
Harmonic, Monogenic and Hypermonogenic Functions on Some Conformally Flat Manifolds in Rn arising from Special Arithmetic Groups of the Vahlen Group
Contemporary Mathematics, Amer. Math. Soc. 370, 159–173 (2005).
(mit D. Constales)
The Bergman Kernels for the half–ball and for fractional wedge–shaped domains in Clifford Analysis
Forum Mathematicum 17, No. 5, 809–821 (2005).
(mit J. Ryan)
Clifford and Harmonic Analysis on Cylinders and Tori
Revista Matemática Iberoamericana 21, 87–110 (2005).
(mit P. Leopardi)
Clifford Algebras, Clifford Analysis and Applications (Editorial Preface)
Bulletin of the Belgian Mathematical Society 11, No. 5, i–ii (2004).
Generalized Analytic Automorphic Forms for some Arithmetic Congruence subgroups of the Vahlen group on the n–Dimensional Hyperbolic Space
Bulletin of the Belgian Mathematical Society 11, No. 5, 759–774 (2004).
The Multiplication of the Clifford–analytic Eisenstein Series
Journal of Number Theory 102, 353–382 (2003).
(mit T. Hempfling)
Order Theory for Isolated Points of Monogenic Functions
Archiv der Mathematik 80, 406–423 (2003).
(mit D. Constales)
Closed formulas for singly–periodic monogenic cotangent, cosecant and cosecant–squared functions in Clifford Analysis
Journal of the London Mathematical Society 67, No. 2, 401–416 (2002).
Monogenic Modular Forms in Two and Several Real and Complex Vector Variables
Computational Methods and Function Theory 2, No. 2, 299–318 (2002).
Eisenstein Series in Complexified Clifford Analysis
Computational Methods and Function Theory 2, No. 1, 29–65 (2002).
(mit D. Constales)
Bergman Kernels for rectangular domains and Multiperiodic Functions in Clifford Analysis
Mathematical Methods in the Applied Sciences 25, No. 16–18, 1509–1526 (2002).
(mit D. Constales)
Representation formulas for the general derivatives of the fundamental solution of the Cauchy–Riemann operator in Clifford Analysis and Applications
Zeitschrift für Analysis und ihre Anwendungen 21, No. 3, 579–597 (2002).
Automorphic forms in Clifford analysis
Complex Variables 47, No. 5, 417–440 (2002).
(mit D. Constales)
Szegö and Polymonogenic Bergman Kernels for half–space and strip domains, and Single–periodic Functions in Clifford Analysis
Complex Variables 47, No. 4, 349–360 (2002).
(mit R. Delanghe und H.R. Malonek)
Differentiability of functions with values in some real associative algebras: approaches to an old problem
Bulletin de la Sociètè Royale des Sciences de Liège 70, No. 4–6, 231–249 (2001).
(mit H. R. Malonek)
A characterization of conformal mappings in R4 by a formal differentiability condition
Bulletin de la Sociètè Royale des Sciences de Liège 70, No. 1, 35–49 (2001).
On a new type of Eisenstein series in Clifford analysis
Zeitschrift für Analysis und ihre Anwendungen 20, No. 4, 1007–1029 (2001).
Monogenic multiperiodic functions in Clifford analysis
Complex Variables 46, No. 4, 337–368 (2001).
Generalized Analytic Automorphic Forms in Hypercomplex Spaces
Frontiers in Mathematics, Birkhäuser, Basel, 2004, 184 Seiten [ISBN 3–7643–7059–9]
Eisenstein Series in Clifford Analysis (Dissertation RWTH Aachen) Aachener Beiträge zur Mathematik (Band 28)
Wissenschaftsverlag Mainz, Aachen, 2000, 141 Seiten [ISBN 3–86073–648–5]
A Theory of Modular Forms in Clifford Analysis, their Applications and Perspectives
In: Advances in Analysis and Geometry New Developments Using Clifford Algebras (eds. Tao Qian, T. Hempfling, A. McIntosh und F. Sommen), Trends in Mathematics, Birkhäuser, 2004, 311–343 [ISBN 3–7643–6661–3]
Poincaré Series in Clifford Analysis
In: Clifford Algebras: Application to Mathematics,
Physics, and Engineering (ed. Rafal Ablamowicz), Progress in Mathematical Physics, Birkhäuser, Boston, 2003; Kapitel 5, 75&ndah;90 [ISBN 0–8176–3525–4]
Generalizations of the Complex Analytic Trigonometric Functions to Clifford Analysis by Eisenstein Series
In: Functional–Analytic and complex methods, their interactions, and Applications to Partial Differential Equations (eds. H. Florian et al.), World Scientific, 2001, 438–456 [ISBN 981–02–4764–8]
(mit D. Constales und R. De Almeida)
Growth orders of monogenic functions in the ball
American Institute of Physics Conf. Proc. 936, 2007, pp. 730–733
(mit I. Cação und D. Constales)
On the role of hypergeometric functions in Dirac type equations
American Institute of Physics Conf. Proc. 936, 2007, pp. 726–729
(mit D. Constales)
On the Navier–Stokes equations with Free Convection in 3D triangular symmetric channels
American Institute of Physics Conf. Proc. 936, 2007, pp. 623–626
(mit J. Tolksdorf)
Applications of hyper–complex analysis in Yang–Mills gauge theories
American Institute of Physics Conf. Proc. 936, 2007, pp. 754–757
(mit D. Constales)
Explicit solutions of the stationary Navier–Stokes equation in a class of reflection symmetric domains
in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2006
15.–19. September 2006, Kreta, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2006
(mit J. Ryan)
Analysis of Dirac Operators on some Conformally Flat Manifolds
in: 17th International Conference on the Application of Computer Science and Mathematics in Architecure and Civil Engineering IKM 2006
12.–14. Juli 2006, Weimar [eds. K. Gürlebeck, C. Könke]
(mit I. Cação und D. Constales)
Bessel functions and higher dimensional Dirac type equations
in: 17th International Conference on the Application of Computer Science and Mathematics in Architecure and Civil Engineering IKM 2006
12.–14. Juli 2006, Weimar [eds. K. Gürlebeck, C. Könke]
(mit D. Constales, K. Gürlebeck, W. Sprößig)
Applications of quaternionic analysis in Engineering
in: 17th International Conference on the Application of Computer Science and Mathematics in Architecure and Civil Engineering IKM 2006
12.–14. Juli 2006, Weimar, [eds. K. Gürlebeck, C. Könke]
(mit D. Constales)
On the Navier–Stokes equation with Free Convection in strip domains and 3D triangular channels
in: 17th International Conference on the Application of Computer Science and Mathematics in Architecure and Civil Engineering IKM 2006
12.–14. Juli 2006, Weimar, [eds. K. Gürlebeck, C. Könke]
(mit D. Constales und R. de Almeida)
Asymptotic growth analysis of some PDE related to higher dimensional Dirac type equations Part II
in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2005
16–20 September 2005, Rhodos, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2005 pp. 892–895, [ISBN 3–527–40652–2]
(mit D. Constales und R. de Almeida)
Asymptotic growth analysis of some PDE related to higher dimensional Dirac type equations II
in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2005
16.–20. September 2005, Rhodos, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2005 pp. 133–136, [ISBN 3–527–40652–2]
(mit D. Constales und R. de Almeida)
Asymptotic growth analysis of some PDE related to higher dimensional Dirac type equations I
in: Proceedings of the International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2005
16.–20. September 2005, Rhodos, Griechenland, [eds. T. E. Simos], Wiley VCH, Weinheim 2005, 928–931, [ISBN 3–527–40652–2]
(mit D. Constales)
Applications of hypercomplex Poincaré series to Bergman spaces
in: Proceedings of the International Conference on Numerical and Applied Mathematics ICNAAM 2004
10.–14. September 2004, Chalkis, Griechenland, [eds. T.E. Simos, Ch. Tsitouras], Wiley VCH Weinheim 2004, 490–492. [ISBN 3–527–40563–1]
Conformal Mappings and Szegö Kernels in Quaternions
Diplomarbeit, Lehrstuhl II für Mathematik RWTH Aachen, Aachen, 1998, 116 Seiten
Eisenstein Series in Clifford Analysis
Dissertation, Lehrstuhl II für Mathematik RWTH Aachen, Aachen, 2000, 141 Seiten
Automorphic Forms and Functions in Clifford Analysis and their Applications
Habilitationsschrift, RWTH Aachen, 2003, 171 Seiten
