A **reproducing kernel Hilbert space** is a Hilbert space of functions in which point evaluation is a continuous linear functional. Using spectral measures one makes connection to specific kind of integral kernels.

- projection measure, Bergman kernel?, Bargmann-Segal transform, coherent state. Using reproducing kernels in the context of machine learning is known as the kernel method. In probability theory, the analogues are Markov kernel?s (related to Chapman-Kolmogorov formula? for conditional probabilities), see

monads of probability, measures, and valuations. The analogue for quantum amplitudes is used in derivation of Feynman integral approach, including the formal coherent state path integrals.

- wikipedia: reproducing kernel Hilbert space, Bergman kernel
- N. Aronszajn,
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*Geometric representation theory for unitary groups of operator algebras*, Advances in Mathematics**208**:1 (2007) 299–317 doi arXiv:math.RT/0501057

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