Growth properties of entire functions depending on a parameter

• Autorzy: Stefan Halvarsson
• Języki publikacji: EN

Abstrakty

EN

We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.

Słowa kluczowe

EN

entire function; holomorphic function; relative order; Fenchel transformation

Kategorie tematyczne

• 32A15: Entire functions
• 52A41: Convex functions and convex programs
• 32A10: Holomorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 1
• Strony: 71-96

Daty

wydano

1996

otrzymano

1995-03-20

poprawiono

1995-10-10

Twórcy

autor

Stefan Halvarsson

• Department of Mathematics, Uppsala University, P.O. Box 480, S-751 06 Uppsala, Sweden

Bibliografia

• [1] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-44.
• [2] H. J. Bremermann, On the conjecture of the equivalence of the plurisubharmonic functions and the Hartogs functions, Math. Ann. 131 (1956), 76-86.
• [3] S. Halvarsson, Extension of entire functions with controlled growth, Math. Scand. 74 (1994), 73-97.
• [4] S. Halvarsson, A geometric interpretation of the relative order between entire functions, Arch. Math. (Basel), to appear.
• [5] O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math. 282 (1976), 53-67.
• [6] O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-type and lower (p,q)-type of an entire function, J. Reine Angew. Math. 290 (1977), 180-190.
• [7] C. O. Kiselman, The use of conjugate convex functions in complex analysis, in: Complex Analysis, J. Ławrynowicz and J. Siciak (eds.), Banach Center Publ. 11, PWN, Warszawa, 1983, 131-142.
• [8] C. O. Kiselman, Order and type as measures of growth for convex or entire functions, Proc. London Math. Soc. (3) 66 (1993), 152-186.
• [9] S. G. Krantz, Function Theory of Several Complex Variables, Wiley-Interscience, 1982.
• [10] P. Lelong, Fonctionnelles analytiques et fonctions entières (n variables), Cours d'été de Montréal 1967, Les Presses de l'Université de Montréal, 1968.
• [11] P. Lelong, Plurisubharmonic Functions and Positive Differential Forms, Gordon and Breach, 1968.
• [12] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970.
• [13] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987.
• [14] A. Sadullaev, Plurisubharmonic measures and capacities on complex manifolds, Russian Math. Surveys 36 (4) (1981), 61-119.
• [15] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411-414.