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Hi there -

I'm Manny, a soon to be MSC thesist. I'm looking for a subject to write my thesis about - and recently I was caught by functional differential equations. Is there any neat reference for funtional equations in settings more general than the real line?

Maybe something that reads "Topological Functional Equations" or even in an algebraic setting?

Many thanks in advance,

Manny.

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3 Answers 3

up vote 1 down vote accepted

Try the book "Functional identities" by Bresar, Chebotar, and Martindale. It deals with functional equations in the realm of associative algebras, Lie algebras and Jordan algebras. As I mentioned in one of my previous postings, the area has its own 2010 MSC code, 16R60.

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Primoz - thanks a lot! Functional equations & Lie Algebras sounds like a one way road... Thanks again. M. –  miami.multiplication Sep 20 '12 at 3:26
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For a somewhat older overview, I would recommend "Functional Equations in Several Variables" by J. Aczel and J. Dhombres; a more recent text is "Functional Equations and Inequalities in Several Variables" by S. Czerwik. You may be interested, in particular, by Chapters 7 and 8 (D'Alembert equation on Abelian and topological groups).

No eBooks, regrettably, but books.google.nl gives an extensive preview.

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Thanks a lot Carlo! I'm gonna try to check that out. D'Alembert equation on Abelian groups looks yummy :D Thanks again! M. –  miami.multiplication Sep 20 '12 at 3:25
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please be more precise. would a linear partial differential equation in one time variable and several "space" variables (possibly taken from an infinite dimensional Hilbert space, or a Lie group) would be an example of what you are looking for?

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