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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
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