{
  "id": "math/0603346",
  "version": "v1",
  "published": "2006-03-14T20:03:23.000Z",
  "updated": "2006-03-14T20:03:23.000Z",
  "title": "Oscillation of Fourier transform and Markov-Bernstein inequalities",
  "authors": [
    "Szilard Gy. Revesz",
    "Noli N. Reyes",
    "Gino Angelo M. Velasco"
  ],
  "journal": "Journal of Approximation Theory 145 (2007), 100-110.",
  "doi": "10.1016/j.jat.2006.07.004",
  "categories": [
    "math.CA"
  ],
  "abstract": "Under certain conditions on an integrable function f having a real-valued Fourier transform Tf=F, we obtain a certain estimate for the oscillation of F in the interval [-C||f'||/||f||,C||f'||/||f||] with C>0 an absolute constant. Given q>0 and an integrable positive definite function f, satisfying some natural conditions, the above estimate allows us to construct a finite linear combination P of translates f(x+kq)(with k running the integers) such that ||P'||>c||P||/q, where c>0 is another absolute constant. In particular, our construction proves sharpness of an inequality of H. N. Mhaskar for Gaussian networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-14T20:03:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A38",
      "41A17"
    ],
    "keywords": [
      "inequality",
      "markov-bernstein inequalities",
      "oscillation",
      "absolute constant",
      "finite linear combination"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3346R"
    }
  }
}