A Cauchy-Euler Type Factorization of Operators
Sin-Ei TAKAHASI, Hirokazu OKA, Takeshi MIURA, and Hiroyuki TAKAGI
Source: Tokyo J. of Math.
Volume 31, Number 2
(2008), 489-493.
Abstract
A Cauchy-Euler type factorization property which is closely related with the Hyers-Ulam stability problem is introduced in the algebra of all linear self maps of a commutative algebra without order.
Several examples of linear self maps with such a property are given in this note.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tjm/1233844065
Digital Object Identifier: doi:10.3836/tjm/1233844065
Mathematical Reviews number (MathSciNet):
MR2477885
Zentralblatt MATH identifier:
05545425
References
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Mathematical Reviews (MathSciNet):
MR4076
Jong-Ho Kim and Soon-Yeong Chung, The stability for the Cauchy-Euler differential equations, preprint.
T. Miura, S. Miyajima and S.-E. Takahasi, Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr., 258 (2003), 90--96.
S. M. Ulam, Problem in Modern Mathematics, Wiley, New York, 1964, Chapter VI, Science Editions.
Mathematical Reviews (MathSciNet):
MR280310
S. M. Ulam, Set, Numbers and Universes, Selected Works, Part III, MIT Press, Cambridge, MA, 1974.
Mathematical Reviews (MathSciNet):
MR441664
