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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical study of several complex variables, the Szeg kernel is an integral kernel that gives rise to a reproducing kernel on a natural Hilbert space of holomorphic functions. It is named for its discoverer, the Hungarian mathematician Gábor Szeg . Let be a bounded domain in Cn with C2 boundary, and let A( ) denote the set of all holomorphic functions in that are continuous on . Define the Hardy space H2( ) to be the closure in L2( ) of the restrictions of elements of A( ) to the boundary. The Poisson integral implies that each element of H2( ) extends to a holomorphic function P in .