Lower-dimensional decompositions using complex variables

Wolfgang Tutschke

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 3, page 329-336
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Tutschke, Wolfgang. "Lower-dimensional decompositions using complex variables." Archivum Mathematicum 034.3 (1998): 329-336. <http://eudml.org/doc/248210>.

@article{Tutschke1998,
abstract = {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.},
author = {Tutschke, Wolfgang},
journal = {Archivum Mathematicum},
keywords = {holomorphic solution of functional equations; poly-analytic functions; ordinary differential equations in the complex domain; holomorphic solution of functional equations; poly-analytic functions; ordinary differential equations in the complex domain; lower-dimensional decompositions},
language = {eng},
number = {3},
pages = {329-336},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lower-dimensional decompositions using complex variables},
url = {http://eudml.org/doc/248210},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Tutschke, Wolfgang
TI - Lower-dimensional decompositions using complex variables
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 3
SP - 329
EP - 336
AB - 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.
LA - eng
KW - holomorphic solution of functional equations; poly-analytic functions; ordinary differential equations in the complex domain; holomorphic solution of functional equations; poly-analytic functions; ordinary differential equations in the complex domain; lower-dimensional decompositions
UR - http://eudml.org/doc/248210
ER -

References

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  1. Balk M. B., Polyanalytic functions, Akademie-Verlag Berlin 1991. (1991) Zbl0864.30035MR1184141
  2. Čadek M., Šimša J., Decomposable functions of several variables, Aequat. Mathem., vol.40, 1990, 8-25. (1990) MR1055187
  3. Čadek M., Šimša J., Decompositions of smooth functions of two multidimensional variables, Czechoslovak Mathem. Journ., vol. 41 (116) 1991, 342-358. (1991) MR1105450
  4. Gauchman H., Rubel L. A., Sums of products of functions of x times functions of y , Linear Algebra Appl., vol. 125, 1989, 19-63. (1989) Zbl0695.26007MR1024482
  5. Herold H., Differentialgleichungen im Komplexen, Göttingen 1975. (1975) Zbl0323.34003MR0470293
  6. Hörmander L., Introduction to Complex Analysis in Several Variables Zbl0685.32001
  7. Neuman F., Functions of two variables and matrices involving factorizations, C. R. Math. Rep. Acad. Sci. Canada, vol. 3, 1981, 7-11. (1981) Zbl0449.15009MR0608675
  8. Neuman F., Factorizations of matrices and functions of two variables, Czechoslovak Math. Journ., vol. 32, 1982, 582-588. (1982) Zbl0517.15012MR0682133
  9. Neuman F., Finite sums of products of functions in single variables, Linear Algebra Appl., vol. 134, 1990, 153-164. (1990) Zbl0714.26007MR1060018
  10. Neuman F., Rassias, Th. M., Functions decomposable into finite sums of products (old and new results, problems and trends), Contained in the volume Constantin Caratheodory: An International Tribute (ed. by Th. M. Rassias), 956-963, World Scientific Publ. Co. 1991. (1991) Zbl0738.26003MR1130873
  11. Rassias, Th. M., Šimša J., Finite sums decompositions in Mathematical Analysis, Wiley, Chichester 1995. (1995) Zbl0859.26005MR1339768
  12. Schwartz L., Théorie des distributions, Tome I, Paris 1957. (1957) Zbl0089.09601
  13. Šimša J., Some factorizations of matrix functions in several variables, Arch. Math.(Brno), vol. 28, 1994, 85-94. (1994) MR1201870
  14. Tutschke W., Partielle Differentialgleichungen. Klassische, funktionalanalytische und komplexe Methoden, Teubner-Text Bd. 27, Leipzig 1983. (1983) Zbl0545.35001MR0730943
  15. Tutschke W., Withalm C., Nonholomorphic solutions to ordinary differential equations in the complex domain, Math. Nachr., vol. 144, 1989, 109-117. (1989) MR1037165
  16. Vekua I. N., New methods for solving elliptic equations, Wiley, New York 1967. (1967) Zbl0146.34301MR0212370
  17. Vekua I. N., Generalized analytic functions, 2nd edit. Moscow 1988 (in Russian); Engl. transl. Oxford 1962. (1988) Zbl0698.47036MR0150320

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