Extended Sobolev Scale on ℤⁿ

2023/10/17 by Ognjen Milatovic, Milatovic, Ognjen
Engineering · #FOS: Mathematics #Fatigue and fracture mechanics #Functional Analysis (math.FA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2310.10894

openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In analogy with the definition of ``extended Sobolev scale" on ℝ<sup>n</sup> by Mikhailets and Murach, working in the setting of the lattice ℤ<sup>n</sup>, we define the ``extended Sobolev scale" H^φ(ℤⁿ), where φ is a function which is RO-varying at infinity. Using the scale H^φ(ℤⁿ), we describe all Hilbert function-spaces that serve as interpolation spaces with respect to a pair of discrete Sobolev spaces [H^(s₀)(ℤⁿ), H^(s₁)(ℤⁿ)], with s₀

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