2020/06/15 by Philippe Rambour, Rambour, Philippe, Abdellatif Seghier +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2006.08147
openalex publication_date 2020/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Toeplitz matrices for the study of the fractional Laplacian on a bounded interval. In this work we get a deep link between (--Δ) α ]0,1[ the fractional Laplacian on the interval ]0, 1[ and T N (Φ α) the Toeplitz matrices of symbol Φ α : θ → |1 -- e iθ | 2α when N goes to the infinity and for α ∈]0, 1 2 [∪] 1 2 , 1[. In the second part of the paper we provide a Green function for the fractional equation (--Δ) α ]0,1[ (ψ) = f for α ∈]0, 1 2 [ and f a sufficiently smooth function on [0, 1]. The interest is that this Green's function is the same as the Laplacian operator of order 2n, n ∈ N. Mathematical Subject Classification (2000) Primary 35S05, 35S10,35S11 ; Secondary 47G30.