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arXiv · 2512.21489

Laguerre- and Laplace-weighted integration of mixed-smoothness functions

Dinh Dũng
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Abstract

We investigate the approximation of generalized Laguerre- or Laplace-weighted integrals over $\mathbb{R}^d_+$ or $\mathbb{R}^d$ of functions from generalized Laguerre- or Laplace-weighted Sobolev spaces of mixed smoothness, respectively. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to $n$ integration nodes for functions from these spaces. The upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic corners or hyperbolic crosses in the function domain $\mathbb{R}^d_+$ or $\mathbb{R}^d$, respectively.

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Dinh Dũng. 2025-12-25. Laguerre- and Laplace-weighted integration of mixed-smoothness functions. https://arxiv.org/abs/2512.21489

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