Most times how the dirac delta is defined / used leaves me unsatisfied. I stumbled upon this paper, which addresses one of my concerns in the introduction ; is it worth the time to study it and the referenced publications by the same author? If not, which resources would leave me with a better understanding?
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First and foremost, and book discussing distributions or generalized functions. Try Guide to Distribution Theory and Fourier Transforms by Robert Strichartz if you'd like an easy introduction with a lot of intuition and motivation. Perhaps a good area of mathematics to supplement this understanding with would be functional analysis. My personal favorite introductory book is Kreyszigs. It is more wordy (more explaination) than some of the others I've seen. I'd suggest books over article publications, but that is only because articles might leave a long string of details up to the references. Hope this helps..
Merkh
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