# zbMATH — the first resource for mathematics

Results on some neutrix convolutions of functions and distributions. (English) Zbl 1047.46032
Summary: The neutrix convolution of two locally summable functions or distributions $$f$$ and $$g$$ is defined to be the limit of the sequence $$\{f_n* g\}$$, where $$f_n(x)= f(x) \tau_n(x)$$ and $$\tau_n(x)$$ is a certain function with compact support and the sequence $$\{\tau_n\}$$ converges to the identity function on the real line. The neutrix convolution of the functions $$x_+^r\ln x_+$$ and $$e^{\lambda x}$$ is evaluated for $$r= 0,1,2,\dots$$ and all $$\lambda\neq 0$$. Further neutrix convolutions are then deduced.
##### MSC:
 46F10 Operations with distributions and generalized functions
Full Text: