Diagonal series of rational functions (several variables)

Sławomir Cynk; Piotr Tworzewski

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 1, page 77-83
  • ISSN: 0066-2216

Abstract

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We give representations of Nash functions in a neighbourhood of a polydisc (torus) in ℂ m as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in ℂ m + 1 .

How to cite

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Sławomir Cynk, and Piotr Tworzewski. "Diagonal series of rational functions (several variables)." Annales Polonici Mathematici 59.1 (1994): 77-83. <http://eudml.org/doc/262464>.

@article{SławomirCynk1994,
abstract = {We give representations of Nash functions in a neighbourhood of a polydisc (torus) in $ℂ^m$ as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in $ℂ^\{m+1\}$.},
author = {Sławomir Cynk, Piotr Tworzewski},
journal = {Annales Polonici Mathematici},
keywords = {diagonal series; rational function; Nash function; rationally convex; Hadamard convolution; holomorphic function; diagonal operator},
language = {eng},
number = {1},
pages = {77-83},
title = {Diagonal series of rational functions (several variables)},
url = {http://eudml.org/doc/262464},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Sławomir Cynk
AU - Piotr Tworzewski
TI - Diagonal series of rational functions (several variables)
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 1
SP - 77
EP - 83
AB - We give representations of Nash functions in a neighbourhood of a polydisc (torus) in $ℂ^m$ as diagonal series of rational functions in a neighbourhood of a polydisc (torus) in $ℂ^{m+1}$.
LA - eng
KW - diagonal series; rational function; Nash function; rationally convex; Hadamard convolution; holomorphic function; diagonal operator
UR - http://eudml.org/doc/262464
ER -

References

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  1. [1] L. Bieberbach, Analytische Fortsetzung, Springer, Berlin, 1967. 
  2. [2] S. Cynk, Representations of Nash functions, Astérisque, to appear. Zbl0805.32004
  3. [3] S. Cynk and P. Tworzewski, Diagonal series of rational functions, Ann. Polon. Math. 55 (1991), 57-63. Zbl0798.32009
  4. [4] P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1984), 129-143. Zbl0538.13007
  5. [5] J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67. Zbl0609.12020
  6. [6] B. A. Fuks, Special Topics in the Theory of Analytic Functions of Several Complex Variables, Fizmatgiz, Moscow, 1963 (in Russian). 
  7. [7] H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277. Zbl0175.03903
  8. [8] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäauser, Basel, 1991. 
  9. [9] K. V. Safonov, On conditions for algebraicity and rationality of the sum of a power series, Mat. Zametki 41 (3) (1987), 325-332 (in Russian). Zbl0622.32009
  10. [10] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271. Zbl0717.32006

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