Hyers–Ulam stability of linear differential operator with constant coefficients | Zendy

Miura Takeshi | Zendy; Miyajima Shizuo | Zendy; Takahasi Sin–Ei | Zendy

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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)

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