For Kreín-Feller operators, continuous eigenfunctions have nodal sets dividing the domain into at least 2 and at most n+r-1 subdomains, and eigenfunctions are continuous when a Green function exists.
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Nodal sets and continuity of eigenfunctions of Kre\u{\i}-Feller operators
For Kreín-Feller operators, continuous eigenfunctions have nodal sets dividing the domain into at least 2 and at most n+r-1 subdomains, and eigenfunctions are continuous when a Green function exists.