{
  "abstract": "The goal of this paper is to establish polynomial Fourier decay for images of self-similar measures $μ$ on $\\mathbb{R}^k$ under sufficiently nonlinear real-analytic maps $f \\colon \\mathbb{R}^k \\to \\mathbb{R}^d$. For example, we prove that if $f$ is analytic on $\\mathbb{R}^k$, its graph does not lie in an affine hyperplane in $\\mathbb{R}^{k+d}$, and $μ$ is not supported in an affine hyperplane in $\\mathbb{R}^k$, then the image measure has polynomial Fourier decay. Key steps in the proof include establishing a uniform Lojasiewicz-type inequality for self-similar measures, and using the decay of the Fourier transform of $μ$ outside a very small exceptional set of frequencies. As an application of our results, we prove polynomial Fourier decay for self-conformal measures on $\\mathbb{C}$ for a large class of complex analytic IFSs which are not self-similar but are conjugate to a linear IFS via an analytic map.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.09743",
  "author_total": 2,
  "authors": [
    {
      "name": "Amlan Banaji"
    },
    {
      "name": "Han Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cqjhppjse0xh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.09743",
  "fulltext_url": null,
  "id": "9cqjhppjse0xh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.09743",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7163998804",
  "pdf_url": "https://arxiv.org/pdf/2606.09743",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cqjhppjse0xh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2606.09743",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.09743"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Fourier transform of nonlinear images of self-similar measures: qualitative aspects",
  "title_text": "Fourier transform of nonlinear images of self-similar measures: qualitative aspects",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/9cqjhppjse0xh",
  "venue": "arXiv",
  "versions": []
}