What question did this study set out to answer?

This research aims to examine the sparsity and approximation rates of holomorphic functions in Gaussian Hilbert spaces, particularly in relation to elliptic PDEs.

June 27, 2026SIAM Journal on Mathematical AnalysisOpen Access

Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces

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Authors

CMCarlo MarcatiUniversité Claude Bernard Lyon 1 CSChristoph SchwabETH Zurich JZJakob ZechHeidelberg University

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Implication

Randomized trial investigates approximation rates of holomorphic maps in Gaussian environments, indicating new insights for PDE solutions.

Key Points

This research aims to examine the sparsity and approximation rates of holomorphic functions in Gaussian Hilbert spaces, particularly in relation to elliptic PDEs.
Analyzed the sparsity of Wiener polynomial chaos expansions for holomorphic maps on Gaussian spaces.
Established weighted summability results for the Wiener-Hermite coefficient sequences from affine-parametric expansions.
Applied the findings to coefficient-to-solution maps of second order, divergence-form elliptic PDEs with log-Gaussian diffusion coefficients.
Demonstrated $N$-term approximation rate bounds for input summability exponents $p \in (0,2)$.
The approximation rate bounds are effective for parameter-to-solution maps in elliptic diffusion PDEs with lognormal coefficients.

Cite This Study

Marcati et al. (2026) studied this question.

synapsesocial.com/papers/6a3f6772aea7db3c1953ee09 https://doi.org/10.1137/25m1757186

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Implication

Randomized trial investigates approximation rates of holomorphic maps in Gaussian environments, indicating new insights for PDE solutions.

Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces

Discussion

Member takes

Implication

Key Points

Cite This Study

Sparsity for Infinite-Parametric Holomorphic Functions on Gaussian Spaces

Discussion

Member takes

Implication

Key Points

Cite This Study

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