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• W2299627974 abstract "We prove sharp, two-sided bounds on sums of the form ∑k∈N0d∖Da(T)exp(−∑j=1dajkj), where Da(T):={k∈N0d:∑j=1dajkj≤T} and a∈R+d. These sums appear in the error analysis of tensor product approximation, interpolation and integration of d-variate analytic functions. Examples are tensor products of univariate Fourier–Legendre expansions (Beck et al., 2014) or interpolation and integration rules at Leja points (Chkifa et al., 2013), (Narayan and Jakeman, 2014), (Nobile et al., 2014). Moreover, we discuss the limit d→∞, where we prove both, algebraic and sub-exponential upper bounds. As an application we consider tensor products of Hardy spaces, where we study convergence rates of a certain truncated Taylor series, as well as of interpolation and integration using Leja points." @default.
• W2299627974 created "2016-06-24" @default.
• W2299627974 creator A5024164746 @default.
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• W2299627974 date "2016-07-01" @default.
• W2299627974 modified "2023-10-15" @default.
• W2299627974 title "On tensor product approximation of analytic functions" @default.
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• W2299627974 doi "https://doi.org/10.1016/j.jat.2016.02.006" @default.
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