Journal: Journal of Functional Analysis

Abbreviation

J. Funct. Anal.

Publisher

Elsevier

Journal Volumes

ISSN

0022-1236
1096-0783

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Publications 1 - 10 of 42
  • On the local uniqueness of steady states for the Vlasov-Poisson system
    Item type: Journal Article
    Iacobelli, Mikaela (2024)
    Journal of Functional Analysis
    Motivated by the results of Lemou, Méhats, and Räphael [16] and Lemou [15] concerning the quantitative stability of some suitable steady states for the Vlasov-Poisson system, we investigate the local uniqueness of steady states near these ones. This is inspired by analogous results of Choffrut and Šverák in the context of the 2D Euler equations [6].
  • Optimal hardy weight for second-order elliptic operator: An answer to a problem of Agmon
    Item type: Journal Article
    Devyver, Baptiste; Fraas, Martin; Pinchover, Yehuda (2014)
    Journal of Functional Analysis
  • Extension theorems and a connection to the Erdős-Falconer distance problem over finite fields
    Item type: Journal Article
    Koh, Doowon; Pham, Thang; Vinh, Le Anh (2021)
    Journal of Functional Analysis
    The first purpose of this paper is to provide new finite field extension theorems for paraboloids and spheres. By using the unusual good Fourier transform of the zero sphere in some specific dimensions, which has been discovered recently in the work of Iosevich, Lee, Shen, and the first and second listed authors (2018), we provide new L2→Lr extension estimates for paraboloids in certain odd dimensions with −1 non-square, which improves significantly the recent exponent obtained by the first listed author. In the case of spheres, we introduce a way of using the first association scheme graph to analyze energy sets, and as a consequence, we obtain new Lp→L4 extension theorems for spheres of primitive radii in odd dimensions, which break the Stein-Tomas result toward Lp→L4 which has stood for more than ten years. Most significantly, it follows from the results for spheres that there exists a different extension phenomenon between spheres and paraboloids in odd dimensions, namely, the Lp→L4 estimates for spheres with primitive radii are much stronger than those for paraboloids. The second purpose is to show that there is a connection between the restriction conjecture associated to paraboloids and the Erdős-Falconer distance conjecture over finite fields. The last is to prove that the Erdős-Falconer distance conjecture holds in odd dimensional spaces when we study distances between two sets: one set lies on a variety (a paraboloid or a sphere), and the other set is arbitrary in vector spaces over finite fields.
  • Structure preservation via the Wasserstein distance
    Item type: Journal Article
    Bartl, Daniel; Mendelson, Shahar (2025)
    Journal of Functional Analysis
  • Asymptotics of Cheeger constants and unitarisability of groups
    Item type: Journal Article
    Gerasimova, Maria A.; Gruber, Dominik; Monod, Nicolas; et al. (2020)
    Journal of Functional Analysis
  • Block-diagonalization of infinite-volume lattice Hamiltonians with unbounded interactions
    Item type: Journal Article
    del Vecchio, Simone; Fröhlich, Jürg; Pizzo, Alessandro (2023)
    Journal of Functional Analysis
    In this paper we extend the local iterative Lie-Schwinger block-diagonalization method – introduced in [8] for quantum lattice systems with bounded interactions in arbitrary dimension– to systems with unbounded interactions, i.e., systems of bosons. We study Hamiltonians that can be written as the sum of a gapped operator consisting of a sum of on-site terms and a perturbation given by relatively bounded (but unbounded) interaction potentials of short range multiplied by a real coupling constant t. For sufficiently small values of |t| independent of the size of the lattice, we prove that the spectral gap above the ground-state energy of such Hamiltonians remains strictly positive. As in [8], we iteratively construct a sequence of local block-diagonalization steps based on unitary conjugations of the original Hamiltonian and inspired by the Lie-Schwinger procedure. To control the supports of the effective potentials generated in the course of our block-diagonalization steps, we use methods introduced in [8] for Hamiltonians with bounded interactions potentials. However, due to the unboundedness of the interaction potentials, weighted operator norms must be introduced, and some of the steps of the inductive proof by which we control the weighted norms of the effective potentials require special care to cope with matrix elements of unbounded operators. We stress that no “large-field problems” appear in our construction. In this respect our operator methods turn out to be an efficient tool to separate the low-energy spectral region of the Hamiltonian from other spectral regions, where the unbounded nature of the interaction potentials would become manifest.
  • Regularity theory for general stable operators: Parabolic equations
    Item type: Journal Article
    Fernández-Real, Xavier; Ros-Oton, Xavier (2017)
    Journal of Functional Analysis
  • A variational approach to S1-harmonic maps and applications
    Item type: Journal Article
    Gaia, Filippo; Rivière, Tristan (2023)
    Journal of Functional Analysis
    We present a renormalization procedure for the Dirichlet Lagrangian for maps from surfaces with or without boundary into S1, whose finite energy critical points are the S1-harmonic maps with isolated singularities. We give some applications of this renormalization scheme in two different frameworks. The first application has to do with the renormalization of the Willmore energy for Lagrangian singular immersions into Kähler-Einstein surfaces while the second application is dealing with frame energies for surfaces immersions into Euclidian spaces.
  • Absolute continuity of Wasserstein geodesics in the Heisenberg group
    Item type: Journal Article
    Figalli, Alessio; Juillet, Nicolas (2008)
    Journal of Functional Analysis
  • Metric currents and Alberti representations
    Item type: Journal Article
    Schioppa, Andrea (2016)
    Journal of Functional Analysis
Publications 1 - 10 of 42