Lower-dimensional decompositions using complex variables (Q2716317)
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scientific article; zbMATH DE number 1602664
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lower-dimensional decompositions using complex variables |
scientific article; zbMATH DE number 1602664 |
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10 June 2001
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holomorphic solution of functional equations
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poly-analytic functions
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ordinary differential equations in the complex domain
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lower-dimensional decompositions
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Lower-dimensional decompositions using complex variables (English)
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In the early 80's, \textit{F. Neuman} solved the problem when a given two-place function is representable as a finite sum of products of factors in single variables [C. R. Math. Acad. Sci., Soc. R. Can. 3, 7-11 (1981; Zbl 0449.15009); Czech. Math. J. 32(107), 582-588 (1982; Zbl 0517.15012)].NEWLINENEWLINENEWLINEThe author of the present paper presents some contributions of Complex Analysis to this decomposition problem (for functions depending on one or several complex variables) by using the concept of partial complex derivatives. For example, he finds conditions on which a given non-holomorphic function \(h=h(z)\) can be represented as \(h(z)=\sum _{k=1}^{n} f_k(z)\bar g_k(z)\), where \(f_k\) and \(g_k\) are holomorphic and \(\;\bar {} \) denotes complex conjugation.
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