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On Fueter-Hurwitz regular mappings

CONTENTSIntroduction........................................................................................................6I. Quaternionic regular and biregular functions in the sense of Fueter..............9   1. Introduction................................................................................................9   2. Fueter derivative and regular functions.....................................................10   3. Quaternionic partial derivatives.................................................................12   4....

On Clifford-type structures

We study several techniques which are well known in the case of Besov and Triebel-Lizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three important decomposition theorems. We deal with so-called atomic, subatomic and wavelet decompositions. All these theorems have much in common. Roughly speaking, they say that a function f belongs to some function space (say S p , q r ̅ A ) if, and only if, it can be decomposed as f ( x ) = ν m λ ν m a ν m ( x ) , convergence in S’, with coefficients...

Pairs of Clifford algebras of the Hurwitz type

Wiesław Królikowski — 1996

Banach Center Publications

For a given Hurwitz pair [ S ( Q S ) , V ( Q V ) , o ] the existence of a bilinear mapping : C ( Q S ) × C ( Q V ) C ( Q V ) (where C ( Q S ) and C ( Q V ) denote the Clifford algebras of the quadratic forms Q S and Q V , respectively) generated by the Hurwitz multiplication “o” is proved and the counterpart of the Hurwitz condition on the Clifford algebra level is found. Moreover, a necessary and sufficient condition for "⭑" to be generated by the Hurwitz multiplication is shown.

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