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Everything about Reproducing kernel Hilbert space

In functional analysis, a Hilbert space

In functional analysis, a discipline within mathematics, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space of functions from a set is an RKHS if the point-evaluation functional, , is continuous for every. Equivalently, is an RKHS if for every there exists a function such that, for all ,The function is then called the reproducing kernel, and it reproduces the value of at via the inner product. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Reproducing kernel Hilbert spaceA 5-minute orientation
  2. Skim a recent paper: Fast Vehicle Routing via Knowledge Transfer in a Reproducing Kernel Hilbert SpaceInfluential work since 2022
  3. Pick up a classic book: Recent Progress on Operator Theory and Approximation in Spaces of Analytic FunctionsThe most-reprinted book on the subject
  4. Read the landmark paper: A reproducing kernel Hilbert space approach to functional linear regressionCited 222 times
  5. Go sideways: Mercer's theoremA closely related topic
  6. Go sideways: Representer theoremA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Definition
  2. Examples
  3. Moore–Aronszajn theorem
  4. Integral operators and Mercer's theorem
  5. Feature maps
  6. Properties
  7. Common examples
  8. Extension to vector-valued functions
  9. Connection between RKHSs and the ReLU function

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics