The nonexistence of regularization operators.
With references to applications in physics the author discusses the well known problem of regularization of generalized functions. As is known, there exist various procedures to regularize some concrete classes of generalized functions. For generalized functions on the real line the author shows that there cannot exist a unique procedure which provides continuous regularization of all the generalized function (under a certain definition of what regularization is). The author also develops these ideas to prove the nonexistence of continuous restrictions into spaces of distributions defined on a closed set. The latter, as the author observes, is important in the study of integral equations in spaces of generalized functions.
scientific article; zbMATH DE number 2003884