Conjugate Harmonic Functions and Clifford Algebras

On primitives and conjugate harmonic pairs in Hermitean Clifford analysis

The notion of a conjugate harmonic pair in the context of Hermitean Clifford analysis is introduced as a pair of specific harmonic functions summing up to a Hermitean monogenic function in an open region Ω of C. Under certain geometric conditions on Ω the conjugate harmonic to a given specific harmonic is explicitly constructed and the potential or primitive of a Hermitean monogenic function is...

Some notes on harmonic and holomorphic functions

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, where “holomorphic” refers to ordinary complex analysis in dimension 2 and generalizations using quaternions and Clifford algebras in higher dimensions. Among the principal themes are weak solutions, the mean-value property, and subharmonicity.

Derivations on Certain Semigroup Algebras

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

p-Analog of the Semigroup Fourier-Steiltjes Algebras

In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

Extending Functions in the Model Subspaces of H^2(R) to C