I apologize in advance that I do not really have any single source to point to, but in general in the articles that I have been reading about mathematical physics, kernels have been appearing nearly everywhere. My background is mostly in algebra and discrete mathematics so I am aware of the numerous isomorphism theorems (and the such) involving kernels of some mapping. Having said that, I am still learning about the basics of PDEs, so it could be that a qualitative answer to my question is waiting me in some lecture note. But I am still interesting in hearing why kernels are interesting with PDEs. Is it due to the structure established by linear algebra and algebra, so that we can view everything as mappings between some structures or is there more to it? Thanks!
2026-04-07 11:00:55.1775559655
What makes kernels of PDEs interesting?
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