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1 results

  • A reproducing kernel approach to Lebesgue decomposition

  • Part of
  • Jashan Bal, Robert T.W. Martin, Fouad Naderi
  • Journal:
    Canadian Journal of Mathematics , First View
    Published online by Cambridge University Press:
    13 May 2024, pp. 1-41
    • Article
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  • We show that properties of pairs of finite, positive, and regular Borel measures on the complex unit circle such as domination, absolute continuity, and singularity can be completely described in terms of containment and intersection of their reproducing kernel Hilbert spaces of “Cauchy transforms” in the complex unit disk. This leads to a new construction of the classical Lebesgue decomposition and proof of the Radon–Nikodym theorem using reproducing kernel theory and functional analysis.