{
  "abstract": "We consider the recovery of functions of the weighted Wiener classes $W_s^μ$ from perturbed Fourier--Hermite coefficients in the metric of $L_\\infty(\\mathbb R)$. For the summation methods of the class $\\mathcal S^θ$ we find error estimates on $W_s^μ$. The estimates take into account the behaviour of the Hermite functions both in the oscillatory region and near the turning point: the maxima of functions with different indices are attained at different points, and the supremum of a sum over a block of indices is substantially smaller than the sum of the suprema. Owing to this, in particular, we establish a common lower bound for all finite diagonal methods; for $s\\ne4/3$ and $p\\ne4/3$ it matches the upper bound and gives the exact order of the error in this class, while at the critical points the gap between the bounds does not exceed $(\\log(e/δ))^{1/4}$ up to a constant. If, in addition, $s>4/3$ or $p<4/3$, then this order is also optimal among all recovery operators that use the whole sequence of data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15610",
  "author_total": 2,
  "authors": [
    {
      "name": "S. G. Solodky"
    },
    {
      "name": "Y. A. Volynets"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xymkr0jvtwbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15610",
  "fulltext_url": null,
  "id": "9xymkr0jvtwbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15610",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7221822060",
  "pdf_url": "https://arxiv.org/pdf/2610.15610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xymkr0jvtwbr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Diagonal recovery from noisy Fourier--Hermite coefficients: exact orders of the error",
  "title_text": "Diagonal recovery from noisy Fourier--Hermite coefficients: exact orders of the error",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9xymkr0jvtwbr",
  "venue": "arXiv",
  "versions": []
}