nLab reproducing kernel Hilbert space




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.

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
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  • J. H. Rawnsley, Coherent states and Kähler manifolds, Quart. J. Math. Oxford (2), 28 (1977) 403–415
  • V. V. Kisil, Integral representations and coherent states, Bulletin of the Belgian Mathematical Society, v. 2 (1995), No 5, pp. 529-540.
  • Daniel Beltiţă, José E. Galé, Universal objects in categories of reproducing kernels, Rev. Mat. Iberoamericana 27:1 (2011) 123–179 arXiv:0912.0091 MR2815734 euclid
  • Daniel Beltiţă, Tudor S. Ratiu, Geometric representation theory for unitary groups of operator algebras, Advances in Mathematics 208:1 (2007) 299–317 doi arXiv:math.RT/0501057

Last revised on April 7, 2023 at 14:11:47. See the history of this page for a list of all contributions to it.