6 Conclusion This paper was devoted to treating a single convolution equation and a spe- cific system of convolution equations; many statistical models with various independence conditions give rise to such equations; measurement error is em- phasized here, but equations of this type are also applicable in other models, such as factor models and panel data models; many examples are presented in Zinde-Walsh (2012). The results of this paper indicate conditions for identification and well-posedness when casting these equations in terms of generalized functions; the generalized functions approach enlarges the area of applicability of the models. References [1] An, Y, and Y. Hu (2012) Well-posedness of measurement error models for self-reported data, Journal of Econometrics, vol. 168 (2012), pp. 259- 269. [2] Antosik, P., J.Mikusinski and R. Sikorski, (1973) Theory of Distribu- tions. The Sequential approach. Elsevier-PWN, Amsterdam-Warszwa. [3] Carroll, R. J., Ruppert, D., Stefanski, L. A. and C.M. Crainiceanu (2006). Measurement Error in Nonlinear Models: A Modern Perspec- tive. Chapman & Hall. 68