Geodesic
Lower-dimensional decompositions using complex variables
Archivum mathematicum, Tome 34 (1998) no. 3, pp. 329-336

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The purpose of the present paper is to represent non-holomorphic functions depending on one or several complex variables by holomorphic and anti-holomorphic functions depending on only one complex variable. Similarly as in the case of functions of real variables, the obtained criteria can also be interpreted as conditions for the solvability of functional equations.
Classification : 30D05, 30G20, 39B32
Keywords: holomorphic solution of functional equations; poly-analytic functions; ordinary differential equations in the complex domain 
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     author = {Tutschke, Wolfgang},
     title = {Lower-dimensional decompositions using complex variables},
     journal = {Archivum mathematicum},
     pages = {329--336},
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     url = {http://geodesic.mathdoc.fr/item/ARM_1998__34_3_a0/}
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Tutschke, Wolfgang. Lower-dimensional decompositions using complex variables. Archivum mathematicum, Tome 34 (1998) no. 3, pp. 329-336. http://geodesic.mathdoc.fr/item/ARM_1998__34_3_a0/