References for functional equations in more general settings than the reals - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T15:38:43Z http://mathoverflow.net/feeds/question/107516 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107516/references-for-functional-equations-in-more-general-settings-than-the-reals References for functional equations in more general settings than the reals miami.multiplication 2012-09-18T23:21:42Z 2012-09-20T06:46:59Z <p>Hi there -</p> <p>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?</p> <p>Maybe something that reads "Topological Functional Equations" or even in an algebraic setting?</p> <p>Many thanks in advance,</p> <p>Manny.</p> http://mathoverflow.net/questions/107516/references-for-functional-equations-in-more-general-settings-than-the-reals/107548#107548 Answer by Delio Mugnolo for References for functional equations in more general settings than the reals Delio Mugnolo 2012-09-19T10:41:29Z 2012-09-20T06:46:59Z <p>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?</p> http://mathoverflow.net/questions/107516/references-for-functional-equations-in-more-general-settings-than-the-reals/107610#107610 Answer by Carlo Beenakker for References for functional equations in more general settings than the reals Carlo Beenakker 2012-09-19T19:09:14Z 2012-09-19T19:09:14Z <p>For a somewhat older overview, I would recommend <em>"Functional Equations in Several Variables"</em> by J. Aczel and J. Dhombres; a more recent text is <em>"Functional Equations and Inequalities in Several Variables"</em> by S. Czerwik. You may be interested, in particular, by Chapters 7 and 8 (D'Alembert equation on Abelian and topological groups).</p> <p>No eBooks, regrettably, but books.google.nl gives an extensive preview.</p> http://mathoverflow.net/questions/107516/references-for-functional-equations-in-more-general-settings-than-the-reals/107611#107611 Answer by Primoz for References for functional equations in more general settings than the reals Primoz 2012-09-19T19:33:26Z 2012-09-19T19:33:26Z <p>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. </p>