Functional Equations: History, Applications and Theory

Abstract

Essays.- 1. On history, applications and theory of functional equations (Introduction).- 2. The esthetics and usefulness of functional equations.- 3. On the historical role of functional equations.- 4. Functional equation methods applied to economic problems: some examples.- 5. On multiple uses of some classical equations.- 6. On some unexpected theoretical and practical applications of functional equations.- 7. Functional equations on groupoids and related structures.- Papers.- 1. Some recent applications of functional equations.- 2. Groupoids with ?-kernels.- 3. The regularity of solutions of functional equations and hypoellipticity.- 4. An improvement of the Nevanlinna-Polya theorem.- 5. On polynomials in additive and multiplicative functions.- 6. Truncations of distribution functions.- 7. Kurepa's functional equation on Gaussian semigroups.- 8. Some recent results on information measures, a new generalization and some 'real life' interpretations of the 'old' and new measures.- 9. On a characterization of the Shannon concentration measure.- 10. Closed invariant curves of a noncontinuously differentiate recurrence.- 11. Invariant curves as solutions of functional equations.- 12. The cycle theorem for flows.