Hypercomplex algebras, hypercomplex analysis and conformal invariance
Generalized Schwarzian derivatives for generalized fractional linear transformations
Generalizations of the classical Schwarzian derivative of complex analysis have been proposed by Osgood and Stowe [12, 13], Carne [5], and Ahlfors [3]. We present another generalization of the Schwarzian derivative over vector spaces.
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Clifford and harmonic analysis on cylinders and torii.
Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...
Dirac operators, conformal transformations and aspects of classical harmonic analysis.
Rarita-Schwinger type operators on spheres and real projective space
In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger...
Some sharp inequalities for Dirac type operators.
Monogenic functions in conformal geometry.
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