A study of bornological properties of the space of entire functions represented by multiple Dirichlet series

• Autorzy: Abdul-Hussein M. S. , Srivastava G. S.
• Języki publikacji: EN

Abstrakty

EN

The space of entire functions represented by Dirichlet series of several complex variables has been studied by S. Dauod [1]. M.D. Patwardhan [6] studied the bornological properties of the space of entire functions represented by power series. In this work we study the bornological aspect of the space Γ of entire functions represented by Dirichlet series of several complex variables. By Γ we denote the space of all analytic functions α (s1, s2) = , having finite abscissa of convergence. We introduce bornologies on&Gamma and Γ and prove that Γ is a convex bornological vector space which is the completion of the convex bornological vector space Γ.

Słowa kluczowe

EN

convex bornological vector space; Dirichlet series

PL

przestrzeń wektorowa; szereg Dirichleta

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 135--150
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Abdul-Hussein M. S.

• Department of Mathematics, Indian Institute of Technology, Roorkee, Roorkee - 247 667, India

autor

Srivastava G. S.

• Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee - 247 667, India

Bibliografia

• [1] S. Daoud, Entire functions represented by Dirichlet series of two complex variables, Port. Math., 43,(1985-1986),407-415.
• [2] F.L Geche, On the region of convergence of a multiple Dirichlet series, Izvestiya VUZ. Matematika, 22(2)(1978), 15-25.
• [3] V.P. Gromov, On the theorey of multiple Dirichlet series, IZV. AN. Arm. ssr ser. fiz, matem, n-, 5(5)(1970), 449-458.
• [4] H. Hogbe-Nlend, Thorie des Boniologies et Applications, Lecture Notes. Springer-Verlag, Berlin, 213(1971).
• [5] H. Hogbe-Nlend, Bornologies and Functional Analysis, North-Holland publishing company, Netherlands, 6(1977).
• [6] M.D. Patwardhan, Study on bornological properties of the space of integral functions, Indian J. Pure Appl. Math., 12(7)(1981), 865-873.