This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results.
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"The book yields a beautiful example of how the advanced methods of abstract harmonic analysis can be employed in the field of functional equations." Mathematical Reviews, 1992
Presents a unified treatment for a branch of the theory of functional equations, the main idea being to use the fundamental results about spectral synthesis on discrete abelian groups. Acidic paper. Annotation copyright Book News, Inc. Portland, Or.
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