On Convergence in Norm of Functions in Lᵖ Spaces by Convolution Using Dilation Kernel

Key Points

• Convergence in norm of functions in L^p spaces is achieved through convolution with a dilation kernel.
• Using the dilation kernel as approximation identity, the study demonstrates convergence for 1≤p<∞ and p=∞.
• The proof highlights the effectiveness of dilation kernels in establishing convergence in different norms.
• This work may enable deeper insights into functional analysis and approximation techniques in mathematical spaces.