Segal–Bargmann space
In mathematics, the Segal–Bargmann space (for Irving Segal and Valentine Bargmann), also known as the Bargmann space or Bargmann–Fock space, is the space of holomorphic functions F in n complex variables satisfying the square-integrability condition: ‖ F ‖ 2 := π − n ∫ C n | F ( z ) | 2 exp ( − | z | 2 ) d z < ∞ , {\displaystyle \|F\|^{2}:=\pi ^{-n}\int _{\mathbb {C} ^{n}}|F(z)|^{2}\exp(-|z|^{2})\,dz<\infty ,} where here dz denotes the 2n-dimensional Lebesgue measure on C n . {\displaystyle \mathbb {C} ^{n}.} It is a Hilbert space with respect to the associated inner product: ⟨ F ∣ G ⟩ = π − n ∫ C n F ( z ) ¯ G ( z ) exp ( − | z | 2 ) d z .