Continuous linear right inverses for convolution operators in spaces of real analytic functions

Michael Langenbruch

Studia Mathematica (1994)

  • Volume: 110, Issue: 1, page 65-82
  • ISSN: 0039-3223

Abstract

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We determine the convolution operators T μ : = μ * on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).

How to cite

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Langenbruch, Michael. "Continuous linear right inverses for convolution operators in spaces of real analytic functions." Studia Mathematica 110.1 (1994): 65-82. <http://eudml.org/doc/216099>.

@article{Langenbruch1994,
abstract = {We determine the convolution operators $T_μ := μ*$ on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).},
author = {Langenbruch, Michael},
journal = {Studia Mathematica},
keywords = {convolution operators; right inverse; Fourier transform},
language = {eng},
number = {1},
pages = {65-82},
title = {Continuous linear right inverses for convolution operators in spaces of real analytic functions},
url = {http://eudml.org/doc/216099},
volume = {110},
year = {1994},
}

TY - JOUR
AU - Langenbruch, Michael
TI - Continuous linear right inverses for convolution operators in spaces of real analytic functions
JO - Studia Mathematica
PY - 1994
VL - 110
IS - 1
SP - 65
EP - 82
AB - We determine the convolution operators $T_μ := μ*$ on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).
LA - eng
KW - convolution operators; right inverse; Fourier transform
UR - http://eudml.org/doc/216099
ER -

References

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