{
  "abstract": "We prove uniform approximation theorems for Chebyshev expansions of continuous functions of two variables. Under a variation-type condition on the square $[-1,1]^2$, a continuous function admits a uniformly convergent Chebyshev expansion in the first variable whose coefficients are continuous functions of the second variable. These results are applied to the spectral graph wavelet transform of time-varying signals on finite weighted graphs: the scaling and wavelet kernels are approximated by expansions with time-varying coefficients whose degrees do not depend on time, the composition of the approximate transform with its adjoint admits the same explicit coefficient formulas as in the time-independent case, and reconstruction by the pseudoinverse is stable, with explicit bounds in terms of the uniform kernel errors. Numerical experiments on a sensor network confirm the convergence and stability estimates. In a denoising problem, soft thresholding of the graph wavelet coefficients with a time-varying transform parameter improves over its time-independent, fixed-parameter counterpart.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09792",
  "author_total": 3,
  "authors": [
    {
      "name": "Davide Bianchi"
    },
    {
      "name": "Sandra Saliani"
    },
    {
      "name": "Dimitrios Vavitsas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c8f838vegfj5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09792",
  "fulltext_url": null,
  "id": "6c8f838vegfj5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09792",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212144365",
  "pdf_url": "https://arxiv.org/pdf/2609.09792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c8f838vegfj5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Uniform Chebyshev approximations of functions satisfying a variation-type condition: reconstruction of time-varying signals on graphs",
  "title_text": "Uniform Chebyshev approximations of functions satisfying a variation-type condition: reconstruction of time-varying signals on graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/6c8f838vegfj5",
  "venue": "arXiv",
  "versions": []
}