Journal: Journal of Fourier Analysis and Applications

Abbreviation

J Fourier Anal Appl

Publisher

Birkhäuser

Journal Volumes

ISSN

1069-5869
1531-5851

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Publications1 - 10 of 10
  • Ridgelet-type Frame Decompositions for Sobolev Spaces related to Linear Transport
    Item type: Journal Article
    Grohs, Philipp (2012)
    Journal of Fourier Analysis and Applications
  • Wavelets on the two-sphere and other conic sections
    Item type: Journal Article
    Antoine, Jean-Pierre; Vandergheynst, Pierre (2007)
    Journal of Fourier Analysis and Applications
  • Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames
    Item type: Journal Article
    Alaifari, Rima; Daubechies, Ingrid; Grohs, Philipp; et al. (2017)
    Journal of Fourier Analysis and Applications
  • Unitarization of the Horocyclic Radon Transform on Homogeneous Trees
    Item type: Journal Article
    Bartolucci, Francesca; De Mari, Filippo; Monti, Matteo (2021)
    Journal of Fourier Analysis and Applications
    Following previous work in the continuous setup, we construct the unitarization of the horocyclic Radon transform on a homogeneous tree X and we show that it intertwines the quasi regular representations of the group of isometries of X on the tree itself and on the space of horocycles.
  • Beurling-Type Density Criteria for System Identification
    Item type: Journal Article
    Aubel, Céline; Bölcskei, Helmut; Vlačić, Verner (2023)
    Journal of Fourier Analysis and Applications
    This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delay-Doppler shifts without a lattice (or other “geometry-discretizing”) constraint on the support set. Concretely, we show that a class of such LTV systems is identifiable whenever the upper uniform Beurling density of the delay-Doppler support sets, measured “uniformly over the class”, is strictly less than 1/2. The proof of this result reveals an interesting relation between LTV system identification and interpolation in the Bargmann-Fock space. Moreover, we show that the density condition we obtain is also necessary for classes of systems invariant under time-frequency shifts and closed under a natural topology on the support sets. We furthermore find that identifiability guarantees robust recovery of the delay-Doppler support set, as well as the weights of the individual delay-Doppler shifts, both in the sense of asymptotically vanishing reconstruction error for vanishing measurement error.
  • A theory of super-resolution from short-time Fourier transform measurements
    Item type: Journal Article
    Aubel, Céline; Stotz, David; Bölcskei, Helmut (2018)
    Journal of Fourier Analysis and Applications
  • Continuous shearlet tight frames
    Item type: Journal Article
    Grohs, Philipp (2011)
    Journal of Fourier Analysis and Applications
  • Uniform Bounds for Oscillatory and Polynomial Carleson Operators
    Item type: Journal Article
    Ramos, João P.G. (2021)
    Journal of Fourier Analysis and Applications
    We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson operators near a single scale version of the quadratic Carleson operator.
  • Stability Estimates for Phase Retrieval from Discrete Gabor Measurements
    Item type: Journal Article
    Alaifari, Rima; Wellershoff, Matthias (2021)
    Journal of Fourier Analysis and Applications
    Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame coefficients is always unstable in infinite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016) and possibly severely ill-conditioned in finite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016). Recently, it has also been shown that phase retrieval from measurements induced by the Gabor transform with Gaussian window function is stable under a more relaxed semi-global phase recovery regime based on atoll functions (Alaifari in Found Comput Math 19(4):869–900, 2019). In finite dimensions, we present first evidence that this semi-global reconstruction regime allows one to do phase retrieval from measurements of bandlimited signals induced by the discrete Gabor transform in such a way that the corresponding stability constant only scales like a low order polynomial in the space dimension. To this end, we utilise reconstruction formulae which have become common tools in recent years (Bojarovska and Flinth in J Fourier Anal Appl 22(3):542–567, 2016; Eldar et al. in IEEE Signal Process Lett 22(5):638–642, 2014; Li et al. in IEEE Signal Process Lett 24(4):372–376, 2017; Nawab et al. in IEEE Trans Acoust Speech Signal Process 31(4):986–998, 1983).
  • Intrinsic Localization of Anisotropic Frames II: alpha-Molecules
    Item type: Journal Article
    Grohs, Philipp; Vigogna, Stefano (2015)
    Journal of Fourier Analysis and Applications
Publications1 - 10 of 10