Diagonal series of rational functions

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

Abstrakty

EN

Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.

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: 1991
• Tom: 55
• Numer: 1
• Strony: 57-63

Daty

wydano

1991

otrzymano

1990-08-27

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, Analytic Extensions, Nauka, Moscow 1967 (in Russian).
• [2] P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1983), 129-143.
• [3] J. Denef and L. Lipshitz, Algebraic power series and diagonals, J. Number Theory 26 (1987), 46-67.
• [4] H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277.
• [5] S. Łojasiewicz, Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish).
• [6] 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).
• [7] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (2) (1990), 227-271.