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Bergman kernel

In the mathematical study of several complex variables, the Bergman kernel, named after Stefan Bergman, is the reproducing kernel for the Hilbert space (RKHS) of all square integrableholomorphic functions on a domain D in C. In detail, let L(D) be the Hilbert space of square integrable functions on D, and let L(D) denote the subspace consisting of holomorphic functions in L(D): that is, L2,h(D)=L2(D)∩H(D){\displaystyle L^{2,h}(D)=L^{2}(D)\cap H(D)}where H(D) is the space of holomorphic functions in D. Then L(D) is a Hilbert space: it is a closed linear subspace of L(D), and therefore complete in its own right.

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