Premium
Hyers–Ulam stability of linear differential operator with constant coefficients
Author(s) -
Miura Takeshi,
Miyajima Shizuo,
Takahasi Sin–Ei
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310088
Subject(s) - mathematics , constant coefficients , linear differential equation , differential operator , constant (computer programming) , stability (learning theory) , operator (biology) , polynomial , degree (music) , differential equation , mathematical analysis , order (exchange) , chemistry , physics , biochemistry , finance , repressor , machine learning , computer science , transcription factor , acoustics , economics , gene , programming language
Let P ( z ) be a polynomial of degree n with complex coefficients and consider the n –th order linear differential operator P ( D ). We show that the equation P ( D ) f = 0 has the Hyers–Ulam stability, if and only if the equation P ( z ) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)