论文标题
用于研究分数laplacian的Toeplitz矩阵
Toeplitz matrices for the study of the fractional Laplacian on a bounded interval
论文作者
论文摘要
toeplitz矩阵，用于研究分数拉普拉斯的矩阵。在这项工作中，我们得到了（ - $δ$）$α$] 0,1 [间隔的分数laplacian] 0，1 [and t n（$φ$ $α$）符号$φ$ $ $α$：$θ$ $ friprow $ | 1 - 2 $α$当n进入无限时，对于$α$ $ \ in $] 0，1 2 [$ \ cup $] 1 2，1 [。在本文的第二部分中，我们为分数方程（ - $δ$）$α$] 0,1 [（$ψ$）= f提供了绿色功能，对于$α$ $ \ in $] $] 0，1 2 [和f在[0，1]上具有足够平滑的功能。兴趣是，该绿色的功能与$ n的laplacian运算符相同。$ n。中学47G30。
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 $Φ$ $α$ : $θ$ $\rightarrow$ |1 -- e i$θ$ | 2$α$ when N goes to the infinity and for $α$ $\in$]0, 1 2 [$\cup$] 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 $α$ $\in$]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 $\in$ N. Mathematical Subject Classification (2000) Primary 35S05, 35S10,35S11 ; Secondary 47G30.
