Diagonal series of rational functions (several variables)

• Autorzy: Sławomir Cynk , Piotr Tworzewski
• Języki publikacji: EN

Abstrakty

EN

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 $ℂ^{m+1}$.

Słowa kluczowe

EN

diagonal series; rational function; Nash function; rationally convex; Hadamard convolution

Kategorie tematyczne

• 32A05: Power series, series of functions
• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 1
• Strony: 77-83

Daty

wydano

1994

otrzymano

1993-04-28

Twórcy

autor

Sławomir Cynk

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

autor

Piotr Tworzewski

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] L. Bieberbach, Analytische Fortsetzung, Springer, Berlin, 1967.
• [2] S. Cynk, Representations of Nash functions, Astérisque, to appear.
• [3] S. Cynk and P. Tworzewski, Diagonal series of rational functions, Ann. Polon. Math. 55 (1991), 57-63.
• [4] P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1984), 129-143.
• [5] J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67.
• [6] B. A. Fuks, Special Topics in the Theory of Analytic Functions of Several Complex Variables, Fizmatgiz, Moscow, 1963 (in Russian).
• [7] H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277.
• [8] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäauser, Basel, 1991.
• [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).
• [10] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271.