On Convergence in Norm of Functions in L^p Spaces by Convolution Using Dilation Kernel

Elin Herlinawati

doi:10.20956/j.v22i1.44148

Authors

Elin Herlinawati Universitas Terbuka

DOI:

https://doi.org/10.20956/j.v22i1.44148

Keywords:

approximation, convolution, convergence in norm, L^p spaces

Abstract

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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