On a generalization of Fueter’s theorem. (English) Zbl 1030.30039
Summary: We discuss a generalization of Fueter’s theorem which states that whenever \(f(x_0,\underline x)\) is holomorphic in \(x_0+\underline x\), then it satisfies \(D\square f=0\), \(D=\partial_{x_0}+ i\partial_{x_1}+ j \partial_{x_2}+ k\partial_{x_3}\) being the Fueter operator.
MSC:
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
References:
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