Annali di Matematica Pura ed Applicata

, Volume 131, Issue 1, pp 281–290 | Cite as

On the coefficients of a function analytic in the unit disc having slow rate of growth

  • G. P. Kapoor
  • A. Nautiyal


For a function f, analytic in z < 1, the notions of generalized orders are introduced that are specially suited for the study of the growth of f, if it is of slow growth. The characterizations of the generalized orders are found in terms of the coefficients in the Taylor series development of f. A decomposition theorem is proved for functions of hirregular growth. The results of the present paper generalize the results in [G. P. Kapoor - K. Gopal, J. Math. Anal. Appl., 74 (1980), pp. 446–455].


Slow Growth Slow Rate Taylor Series Unit Disc Generalize Order 
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  1. [1]
    G. P. Kapoor -K. Gopal,Decomposition theorems for functions analytic in a finite disc having slow rates of growth, J. Math. Anal. Appl.,74 (1980), pp. 446–455.Google Scholar
  2. [2]
    L. K. Sons,Regularity of growth and gaps, J. Math. Anal. Appl.,24 (1968), pp. 296–306.Google Scholar
  3. [3]
    G. Valieon,Fonctions analytiques, Presses Universitaires de France, Paris, 1954.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1982

Authors and Affiliations

  • G. P. Kapoor
    • 1
  • A. Nautiyal
    • 1
  1. 1.Kanpur

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