{
  "abstract": "We study powers and functional calculi of higher-order selfadjoint and skew higher-order selfadjoint operators on complex Hilbert spaces. First, we compare the behavior of their powers with the corresponding theory for $m$-isometries. We prove that if $T$ is invertible and two powers $T^r$ and $T^s$ are, respectively, $m$- and $\\ell$-selfadjoint, then $T^{\\gcd(r,s)}$ is $\\min\\{m,\\ell\\}$-selfadjoint. In particular, invertibility yields the expected converse for consecutive powers. We also show that two consecutive skew $m$-selfadjoint powers must be non-invertible; in fact, nilpotent. For polynomials, we obtain coefficient characterizations under a cardinality assumption on the spectrum. Finally, for holomorphic functions we give spectral characterizations according to whether the spectrum is finite, or the domain of analyticity is a region, and we derive consequences for Möbius transformations and $m$-isometries. Several examples illustrate why the spectral hypotheses cannot be omitted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26572",
  "author_total": 4,
  "authors": [
    {
      "name": "M. Faghih-Ahmadi"
    },
    {
      "name": "T. Bermúdez"
    },
    {
      "name": "K. Hedayatian"
    },
    {
      "name": "H. Zaway"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57v8fy0efwg1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26572",
  "fulltext_url": null,
  "id": "57v8fy0efwg1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26572",
  "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",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7223015167",
  "pdf_url": "https://arxiv.org/pdf/2610.26572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57v8fy0efwg1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26572"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Powers and Functional Calculus for $m$-Selfadjoint and Skew $m$-Selfadjoint Operators",
  "title_text": "Powers and Functional Calculus for m-Selfadjoint and Skew m-Selfadjoint Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/57v8fy0efwg1v",
  "venue": "arXiv",
  "versions": []
}