Matsaev's theorem is a theorem from complex analysis, which characterizes the order and type of an entire function.

The theorem was proven in 1960 by Vladimir Igorevich Matsaev.[1]

Matsaev's theorem

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Let   with   be an entire function which is bounded from below as follows

 

where

  and  

Then   is of order   and has finite type.[2]

References

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  1. ^ Mazaew, Wladimir Igorewitsch (1960). "On the growth of entire functions that admit a certain estimate from below". Soviet Math. Dokl. 1: 548–552.
  2. ^ Kheyfits, A.I. (2013). "Growth of Schrödingerian Subharmonic Functions Admitting Certain Lower Bounds". Advances in Harmonic Analysis and Operator Theory. Operator Theory: Advances and Applications. Vol. 229. Basel: Birkhäuser. doi:10.1007/978-3-0348-0516-2_12.