I'd like to learn about some applications of RKHSs outside of machine learning and statistics. For instance, do they feature in physics (maybe quantum mechanics)? It would good to have a brief explanation of the usage too, if possible.
2026-03-25 09:50:11.1774432211
What are the applications of reproducing kernel Hilbert spaces? (outside of statistics/machine learning)
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There are loads of applications outside machine learning and statistics. Actually the concept of RKHS is more than 100 years old and was originally developed to solve problems in complex analysis. The theory was formalised by Aronszajn in the 50s obviously predating much of modern statistics and machine learning.
Check out the introduction in wikipedia on RKHS or the description of certain prominent RKHS of analytic functions such as Segal-Bargman space or Hardy space. I heard that applications in quantum mechanics involve Fock spaces.
My conclusion on RKHS: They are everywhere!