On relative Ritt L*-type and relative Ritt L*-weak type of entire functions presented in the form of vector valued Dirichlet series

Yıl 2017, Cilt: 5 Sayı: 2, 104 - 111, 30.03.2017

Sanjib Kumar Datta , Tanmay Biswas

Öz

In this paper we introduce the idea of relative Ritt L*-type and relative RittL*-weak type of entire functions represented by vector valued dirichlet series. Further we wish to study some growth properties of entire functions represented by a vector valued  Dirichlet series on the basis of relative Ritt L*-type and relative Ritt L*-weak type.

Anahtar Kelimeler

Vector valued Dirichlet series (VVDS), relative Ritt L*-order, relative Ritt L*-lower order, relative Ritt L*-type, relative Ritt L*-weak type

Kaynakça

• Q. I. Rahaman: The Ritt order of the derivative of an entire function, Annales Polonici Mathematici, Vol. 17 (1965), pp. 137-140.
• C. T. Rajagopal and A. R. Reddy: A note on entire functions represented by Dirichlet series, Annales Polonici Mathematici, Vol. 17 (1965), pp. 199-208.
• J. F. Ritt: On certain points in the theory of Dirichlet series, Amer. Jour. Math., Vol. 50 (1928), pp. 73-86.
• G. S. Srivastava: A note on relative type of entire functions represented by vector valued dirichlet series, Journal of Classicial Analysis, Vol. 2, No. 1 (2013), pp. 61-72.
• G. S. Srivastava and A. Sharma: On generalized order and generalized type of vector valued Dirichlet series of slow growth, Int. J. Math. Archive, Vol. 2, No. 12 (2011), pp. 2652-2659.
• B. L. Srivastava: A study of spaces of certain classes of vector valued Dirichlet series, Thesis, I. I. T., Kanpur, (1983).
• R. P. Srivastav and R. K. Ghosh: On entire functions represented by Dirichlet series, Annales Polonici Mathematici, Vol. 13 (1963), pp. 93-100.
• D. Somasundaram and R. Thamizharasi : A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl. Math., Vol.19 (March 1988), No. 3, pp. 284-293.