Work

Equivalence of the Weighted Fractional Sobolev Space on a Disk with Characterization by the Decay Rate of Fourier–Jacobi Coefficients and K-Interpolation

Year: 2024

Type: article

Abstract: In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in $$\mathbb {R}^{2}$$ R 2 , we establish a characterisation of the weighted Sobolev space $$H_{\gamma }^{s}(\Omega )$$ H γ s ( Ω ) in terms of the decay rate of Fourier–Jacobi coefficients. This framework is then used to give a precise analysis of the solution to the fractional Laplace equation on the unit disk.

Source: Journal of Fourier Analysis and Applications

DOI: 10.1007/s00041-024-10127-6

Author: V. J. Ervin

Institution: Clemson University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funder: Clemson University