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We study the numerical approximation of integrals over $\mathbb{R}^s$ with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of functions.
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C. Irrgeher and G. Leobacher: High-dimensional integration on the ℝ d \mathbb{R}^{d} , weighted Hermite spaces, and orthogonal transforms. J. Complexity 31: 174–205, 2015
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M. Gnewuch, M. Hefter, A. Hinrichs and K. Ritter: Embeddings of weighted Hilbert spaces and Applications to multivariate and infinite-dimensional integration J. Approx. Theory 222
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T. Goda, K. Suzuki, and T. Yoshiki: Optimal order quadrature error bounds for infinite-dimensional higher order digital sequences. T. Found. Comput. Math. (2017). https://doi.org/10.1007/s10208-017-9345-0
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J.F. Traub, G.W. Wasilkowski, and H. Woźniakowski: Information-Based Complexity
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2052
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