Jump to content

Matsaev's theorem

From Wikipedia, the free encyclopedia

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

[edit]

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

[edit]
  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.