# A category of reproducing kernel Hilbert algebras

** Speaker:** Michael Montgomery, Dartmouth College

** Date:** September 21, 2023

** Abstract:** In the talk we will develop a natural definition (in the categorical sense) of an algebra structure on a reproducing kernel Hilbert space. This definition is also equivalent to subconvolutivity of weight functions in examples from harmonic analysis. We will then show the category of reproducing kernel Hilbert algebras (RKHA) is closed under orthogonal sums, tensor products, pushouts, and pullbacks such that the spectrum is a functor compatible with these constructions. Furthermore, the image of the spectrum as a functor from RKHA to Top contains all compact subspaces of R^n, n>0.