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Analysis and applications of holomorphic functions in higher dimensions. (English) Zbl 0808.30029

The hyperholomorphic Clifford-valued functions are considered which generalize the holomorphic functions from the one-dimensional complex analysis. There are written down the associated Taylor formula, Cauchy integral formula, estimates for the Taylor expansions remainder terms, some connections between harmonic and hyperholomorphic functions.
A part of the results proved in the work were presented earlier in, e.g., F. Brackx, R. Delanghe and F. Sommen [Clifford analysis (1982; Zbl 0529.30001)]; H. Malonek [Complex Variables, Theory Appl. 15, No. 3, 181-191 (1990; Zbl 0714.30045)]; R. Delanghe, F. Sommen and V. Souček [Clifford algebra and spinor-valued functions (1992; Zbl 0747.53001)].

MSC:

30G35 Functions of hypercomplex variables and generalized variables
35C10 Series solutions to PDEs
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
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