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This document contains solutions to several problems regarding properties of convolutions and functions in Lp spaces. It proves that: 1) The convolution of functions f in Lp and g in Lp is bounded and continuous. 2) The convolution of a C∞ function with compact support and a function in Lp results in a C∞ function. 3) C∞ functions with compact support that are dense in Lp. 4) Sets of finite positive measure subtracted from themselves contain neighborhoods of the origin. 5) The algebra L1 has no identit

Author

Super Nezh

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EN