References for functional equations in more general settings than the reals - MathOverflow

References for functional equations in more general settings than the reals

2012-09-18T23:21:42Z

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.

Answer by Delio Mugnolo for References for functional equations in more general settings than the reals

2012-09-19T10:41:29Z

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?

Answer by Carlo Beenakker for References for functional equations in more general settings than the reals

2012-09-19T19:09:14Z

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.

Answer by Primoz for References for functional equations in more general settings than the reals

2012-09-19T19:33:26Z

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.