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The space $L^2_{hol}(\\gamma_\\alpha)$ is classically known as the Segal-Bargmann space. We show that $P_\\alpha$ extends to a bounded operator on $L^p(\\gamma_{\\alpha p/2})$, and calculate the exact norm of this scaled $L^p$ Bargmann projection. 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Gryc","submitted_at":"2012-11-26T18:44:09Z","abstract_excerpt":"For $\\alpha>0$, the Bargmann projection $P_\\alpha$ is the orthogonal projection from $L^2(\\gamma_\\alpha)$ onto the holomorphic subspace $L^2_{hol}(\\gamma_\\alpha)$, where $\\gamma_\\alpha$ is the standard Gaussian probability measure on $\\C^n$ with variance $(2\\alpha)^{-n}$. The space $L^2_{hol}(\\gamma_\\alpha)$ is classically known as the Segal-Bargmann space. We show that $P_\\alpha$ extends to a bounded operator on $L^p(\\gamma_{\\alpha p/2})$, and calculate the exact norm of this scaled $L^p$ Bargmann projection. 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