Extremal Functions with Vanishing Condition View Full Text


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Article Info

DATE

2015-10

AUTHORS

Friedrich Littmann, Mark Spanier

ABSTRACT

For a Hermite–Biehler function E of mean type τ, we determine the optimal (with respect to the de Branges measure of E) majorant ME+ and minorant ME- of exponential type τ for the truncation of x↦(x2+a2)-1. We prove that ∫RME+(x)-ME-(x)|E(x)|-2dx=1a2K(0,0),where K is the reproducing kernel for the de Branges space H(E). As an application, we determine the optimal majorant and minorant for the Heaviside function that vanish at a fixed point α=ia on the imaginary axis. We show that the difference of majorant and minorant has integral value (πa-tanh(πa))-1πa. More... »

PAGES

209-229

References to SciGraph publications

  • 2013-04. One-sided approximation in L of the characteristic function of an interval by trigonometric polynomials in PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
  • 1951-12. On Polya frequency functions in JOURNAL D'ANALYSE MATHÉMATIQUE
  • 1994. Topics in Hardy Classes and Univalent Functions in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00365-015-9304-4

    DOI

    http://dx.doi.org/10.1007/s00365-015-9304-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1052737357


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