by László Székelyhidi (University of Debrecen, Hungary)

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.

• The Basic Problems of Spectral Analysis and Spectral Synthesis
• Polynomials and Exponential Polynomials
• Fourier-Transformation and Mean Periodic Functions
• Applications for Functional Equations:
  • Functional Equations for Polynomials
  • The Levi-Civitá Functional Equation
  • D'Alembert-Type Functional Equations
  • Addition and Subtraction Theorems
  • Difference Equations on Semigroups
  • Mean-Value Type Functional Equations
  • Applications for Differential Equations
  • Noncommutative Applications