Geodesic
On a relation between real and holomorphic functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 68-74

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We study $\lambda$-holomorphic functions, which generalize holomorphic functions to the case of arbitrary complex exponent $\lambda$. We establish a connection between such functions and real-valued quadratic forms and prove that for $\lambda\ne\mu$, $\lambda\ne\overline{\mu}$ there are $\lambda$- and $\mu$-holomorphic functions whose imaginary parts coincide identically; such functions are polynomials of degree no greater tan two.
Keywords: partial derivative, $\lambda$-holomorphic function, system of algebraic equations, linear substitution, quadratic form.
Mots-clés : Cauchy–Riemann conditions 
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     author = {V. G. Nikolaev},
     title = {On a relation between real and holomorphic functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {68--74},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a7/}
}
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V. G. Nikolaev. On a relation between real and holomorphic functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 68-74. http://geodesic.mathdoc.fr/item/INTO_2021_195_a7/