Analysis finds convergence in norm of functions in L^p spaces via convolution, suggesting approximation identity benefits.
In this paper, we investigate the convergence in norm of functions in L^p (R^d) by convolution. We use dilation kernel from L^1 as approximation identity and prove convergence of a function using convolution with dilation kernel in norm ‖∙‖_p for 1≤p<∞ and norm ‖∙‖_∞ for p=∞.
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Elin Herlinawati (2025) studied this question.
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