Univariate tight wavelet frames of minimal support Articles uri icon

authors

  • Gómez-Cubillo, F.
  • VILLULLAS MERINO, SERGIO

publication date

  • April 2021

start page

  • 42-1

end page

  • 42-56

issue

  • 2

volume

  • 15

International Standard Serial Number (ISSN)

  • 2662-2033

Electronic International Standard Serial Number (EISSN)

  • 1735-8787

abstract

  • This work characterizes (dyadic homogeneous) wavelet frames for L2(ℝ) by means
    of spectral techniques. These techniques use decomposability properties of the
    frame operator in spectral representations associated with the dilation operator. The
    approach is closely related to usual Fourier domain fberization techniques, dual
    Gramian analysis, and extension principles. Spectral formulas are used to determine
    all the tight wavelet frames for L2(ℝ) with a fxed fnite number of generators of
    minimal support. The method associates wavelet frames of this type with certain
    inner operator-valued functions in Hardy spaces. The cases with one and two generators are completely solved.

subjects

  • Economics

keywords

  • wavelet frames; spectral techniques; hardy spaces; inner functions