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Linear Differential Equations and Logarithmic Derivative Estimates
Author(s) -
Chyzhykov Igor,
Gundersen Gary G.,
Heittokangas Janne
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013965
Subject(s) - mathematics , meromorphic function , corollary , logarithm , logarithmic derivative , mathematical proof , unit disk , derivative (finance) , mathematical analysis , linear differential equation , logarithmic spiral , mathematics subject classification , differential equation , pure mathematics , geometry , financial economics , economics
We prove two sharp inequalities for the growth of solutions of certain linear differential equations in the unit disk. For the proofs of these inequalities, we use the method of successive approximations and sharp estimates for the logarithmic derivatives of finite order meromorphic functions in the unit disk. These techniques can also be used to give an alternate proof of a well‐known result in the plane. The sharp logarithmic derivative estimates are a corollary of general estimates, and all these estimates have independent interest. 2000 Mathematics Subject Classification 34M10, 30D35.