Year: 2026
Type: preprint
Abstract: For integers $α,d \geqslant1$, we determine the best constants in the inequalities $||(a_j)_{j=1}^{d}||_{\ell^1} \leqslant C_{α,d} ||((Δ^αa)_j)_{j=1}^{d+α}||_{\ell^2},$ where $Δ$ is the difference operator. We find that these constants correspond to the $\ell^2$ 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.
Source: arXiv (Cornell University)
Institutions: Lund University, Georgia Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221988109