Abstract
It has recently been shown that operators of a certain type can be used to generalize the concept of a function and to extend the Laplace-transform calculus. A further study of these operators is now undertaken, and some new characterizations of them are obtained. In a preliminary discussion, the notion of an operational calculus is examined from an axiomatic point of view, and a general definition is formulated; systems of generalized functions are also considered axiomatically, and are shown to be necessary for the extension, under mild conditions, of differential operators on functions of a real variable.
Reference4 articles.
1. Hamburger H. L. & Grimshaw M. E. 1951 Linear transformations in n-dimensional vector space.Cambridge University Press.
2. Les fonctions analytiques comme ultra-distributions dans le calcul op�rationnel
3. Weston J. D. 1957 R.C. Circ. mat. Palermo (2) 6 325.
4. Wiener N. 1933 The Fourier integral and certain of its applications. Cambridge University Press.
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献