@inproceedings{ConstalesKrausshar,
  author    = {Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2863},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28639},
  pages     = {10},
  abstract  = {In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{CacaoConstalesKrausshar,
  author    = {Cacao, Isabel and Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2834},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28343},
  pages     = {8},
  abstract  = {Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{GrobConstalesKrausshar,
  author    = {Grob, Dennis and Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {THE HYPERCOMPLEX SZEG{\"O} KERNEL METHOD FOR 3D MAPPING PROBLEMS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2846},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28464},
  pages     = {7},
  abstract  = {In this paper we present rudiments of a higher dimensional analogue of the Szeg{\"o} kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{Krausshar,
  author    = {Kraußhar, Rolf S{\"o}ren},
  title     = {SOME HARMONIC ANALYSIS ON M{\"O}BIUS STRIP DOMAINS AND THE KLEIN BOTTLE IN Rn},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom and Werner, Frank},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2769},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27692},
  pages     = {10},
  abstract  = {The aim of this paper we discuss explicit series constructions for the fundamental solution of the Helmholtz operator on some important examples non-orientable conformally at manifolds. In the context of this paper we focus on higher dimensional generalizations of the Klein bottle which in turn generalize higher dimensional M{\"o}bius strips that we discussed in preceding works. We discuss some basic properties of pinor valued solutions to the Helmholtz equation on these manifolds.},
  subject      = {Angewandte Informatik},
  language  = {en}
}
@inproceedings{KrausshardeAlmeida,
  author    = {Kraußhar, Rolf S{\"o}ren and de Almeida, Regina},
  title     = {FUNDAMENTALS OF A WIMAN VALIRON THEORY FOR POLYMONOGENIC FUNCTIONS},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
  editor    = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2810},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28100},
  pages     = {6},
  abstract  = {In this paper we present some rudiments of a generalized Wiman-Valiron theory in the context of polymonogenic functions. In particular, we analyze the relations between different notions of growth orders and the Taylor coefficients. Our main intention is to look for generalizations of the Lindel¨of-Pringsheim theorem. In contrast to the classical holomorphic and the monogenic setting we only obtain inequality relations in the polymonogenic setting. This is due to the fact that the Almansi-Fischer decomposition of a polymonogenic function consists of different monogenic component functions where each of them can have a totally different kind of asymptotic growth behavior.},
  subject      = {Angewandte Informatik},
  language  = {en}
}