Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 1 h ago
PreprintCC BY 4.0arXiv

A sharp discrete Sobolev inequality and left inverses of higher order differences

  • Raul Hindov
  • Shahaf Nitzan
  • Jan-Fredrik Olsen
  • Eskil Rydhe
Open at sourcePDFDOICite

Abstract

For integers α,d geqslant1, we determine the best constants in the inequalities ||(aj)j=1d||ℓ1 leqslant Cα,d ||((Δαa)j)j=1d+α||ℓ2, where Δ is the difference operator. We find that these constants correspond to the ℓ2 norm of the discrete Chebyshev polynomials, and show that the extremal sequences may be obtained by appropriate sampling of the discrete Landau polynomials. From beginning to end, this project was carried out without use of AI.

Related

  1. Explicit Oblique Inverses of the Approximate Discrete Radon Transform
    Donsub Rim
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. A priori bounds for geodesic diameter. Part III. A Sobolev–Poincaré inequality and applications to a variety of geometric variational problems
    Ulrich Menne, Christian Scharrer
    Duke Mathematical JournalPeer-reviewedLicence not statedFull text8 citedGeneral mathematicsOpenAlex
  3. Sharp Quantitative Stability for the Affine p-Sobolev Inequality, Part II: The Case 1<p<2
    Song Fan, Gui-Dong Li, Jianjun Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Log-Sobolev inequality for 2D SU(N) lattice gauge theory at all couplings
    Jack Piazza, Hao Shen
    arXivPreprintCC0Full textMathematical physicsProbabilityarXiv
  5. Sharp Gradient Stability for the Sobolev Trace Inequality
    Xi-Nan Ma, Yitian Zhang, Yang Zhou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{hindov2026sharp,
  title = {{A sharp discrete Sobolev inequality and left inverses of higher order differences}},
  author = {Raul Hindov and Shahaf Nitzan and Jan-Fredrik Olsen and Eskil Rydhe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19010},
  eprint = {2610.19010},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19010},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A sharp discrete Sobolev inequality and left inverses of higher order differences
AU  - Raul Hindov
AU  - Shahaf Nitzan
AU  - Jan-Fredrik Olsen
AU  - Eskil Rydhe
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19010
UR  - https://arxiv.org/abs/2610.19010
AB  - For integers α,d geqslant1, we determine the best constants in the inequalities ||(a_j)_j=1^d||_ℓ^1 leqslant C_α,d ||((Δ^αa)_j)_j=1^d+α||_ℓ^2, where Δ is the difference operator. We find that these constants correspond to the ℓ^2 norm of the discrete Chebyshev polynomials, and show that the extremal sequences may be obtained by appropriate sampling of the discrete Landau polynomials. From beginning to end, this project was carried out without use of AI.
ER  -