exponential polynomial; extension; linear functional equation
Exponential polynomials are the building bricks of spectral synthesis. In some cases it happens that exponential polynomials should be extended from subgroups to whole groups. To achieve this aim we prove an extension theorem for exponential polynomials which is based on a classical theorem on the extension of homomorphisms.
 E. Hewitt K. Ross: Abstract Harmonic Analysis I., II. Springer-Verlag, Berlin, 1963.
 L. Székelyhidi: Convolution Type Functional Equations on Topological Abelian Groups
. World Scientific, Singapore, 1991. MR 1113488