# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
D’Alembert’s functional equation on compact groups. (English) Zbl 1131.39028

In this paper, dedicated to Themistocles M. Rassias, the author offers an alternative proof to a theorem presented by T.M.K. Davison at the 44th International Symposium on Functional Equations 2006, Louisville KY on the general solution $f:G\to ℂ$ of the functional equation

$f\left(xy\right)+f\left(x{y}^{-1}\right)=2f\left(x\right)f\left(y\right)\phantom{\rule{1.em}{0ex}}\left(x,y\in G\right),$

where $G$ is a compact group. The author’s proof relies heavily on his paper “Spectral synthesis problems on locally compact groups”, that at the time of publication of the paper under review apparently existed only as preprint. In that paper the author offers extension of spectral synthesis from discrete abelian groups to not necessarily abelian compact groups.

##### MSC:
 39B82 Stability, separation, extension, and related topics 43A45 Spectral synthesis on groups, semigroups, etc.
##### Keywords:
compact group; spectral synthesis