{
  "id": "math/0303064",
  "version": "v1",
  "published": "2003-03-05T17:04:00.000Z",
  "updated": "2003-03-05T17:04:00.000Z",
  "title": "Rearrangements of Trigonometric Series and Trigonometric Polynomials",
  "authors": [
    "S. V. Konyagin"
  ],
  "categories": [
    "math.CA",
    "math.CO"
  ],
  "abstract": "The paper is related to the following question of P.~L.~Ul'yanov: is it true that for any $2\\pi$-periodic continuous function $f$ there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of $f$ decrease. Also, we study a problem how to choose $m$ terms of a trigonometric polynomial of degree $n$ to make the uniform norm of their sum as small as possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-03-05T17:04:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A20",
      "42A05",
      "42A61"
    ],
    "keywords": [
      "trigonometric polynomial",
      "trigonometric series",
      "trigonometric fourier series",
      "periodic continuous function",
      "uniformly convergent rearrangement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3064K"
    }
  }
}