A Bergman kernel is a function of a complex variable with the "reproducing kernel" property defined for any domain
in which there exist nonzero analytic
functions of class 
with respect to the Lebesgue measure 
.
Bergman Kernel
Explore with Wolfram|Alpha
References
Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, pp. 356-357, 1988.Referenced on Wolfram|Alpha
Bergman KernelCite this as:
Weisstein, Eric W. "Bergman Kernel." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BergmanKernel.html