A criterion of joint C-differentiability and a new proof of Hartog's main theorem

• Autorzy: Dzagnidze O.
• Języki publikacji: PL

Abstrakty

EN

A necessary and sufficient condition is established for a complex-valued function to be jointly C-differentiable at a given point by applying Hartog's main theorem.

Słowa kluczowe

EN

jointly C-differentiable; jointly C-holomorphic; jointly C-analytic; separately C-holomorphic; separatly C-analytic

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2007
• Tom: Vol. 13, nr 1
• Strony: 13--17
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Dzagnidze O.

• Georgian Academy of Sciences. A. Rozmadze Mathematical Institute, 1, M. Aleksidze St., Tbilisi 0193, Georgia,

Bibliografia

• [1] Cartan, H., Theorie elementaire des fonctions analytiques d'une au plusieurs variables complexes, A vec le concours de Reiji Takahashi Enseignement des Sciences,Hermann, Paris, 1961.
• [2] Dzagnidze, O., A necessary and sufficient condition for differentiability functions of several variables, Proc. A. Razmadze Math. Inst. 123 (2000), 23-29.
• [3] Dzagnidze, O., Same new results on the continuity and differentiability of functions of several real variables, Proc. A. Razmadze Math. Inst. 134 (2004), 1-138.
• [4] Hartogs, F ., Zur Theorie der analytischen Funktionen mehrerer unabhuengiger Veranderlichen, insbesondere ueber die Darstellung derselben durch Reihen, welche nach Potenzen einer Veranderlichen fortschreiten, Math Ann. 62 (1906), 1-88.
• [5] Menchoff, D., Les conditions de monogeneite, Actualites Scientifiques et Industrielles 329 (1936), Hermann, Paris, 1-52.
• [6] Saks, S., Theory of the Integral, "Monografie Matematyczne" Ser. 7, Polish Math. Soc., Warszawa-Lwow, 1937.
• [7] Shabat, B. V ., Introduction to Complex Analysis, Part II. Functions of a Several Variables (in Russian), Nauka, Moscow, 1976.
• [8] Tolstov, G., Sur les fonctions bornees verifiant les conditions de Cauchy-Riemann, Mat. Sb. 10(52)(1-2) (1942), 79-85.