On Some Fractional order Binomial sequence spaces with infinite Matrices

Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices

In this short paper, we review the Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices. We derive the rotations by any angle through the spectral behavior of the fractional powers of the rotation matrix by $\fracπ{2}$ in $\mathbb{R}^3$ about some axis.

矩阵分数次幂的数值半径

The numerical radius of fractional powers of matrices

本文利用分数次幂积分表示与扇形矩阵几何性质，证明增生-耗散矩阵满足 ω(A^t)≥ω^t(A)，并推广到增生矩阵在 0<t<1/2 时的情形。

Fractional ordered Euler Riesz sequence space

The main objective of this article is to introduce Euler-Riesz difference sequence spaces of fractional order $τ $ along with infinite matrices. Some topological properties of these spaces are considered here along with the Schauder basis, $α -,β-$ and $γ-$duals of the spaces. Keywords: Euler-Riesz difference sequence space, difference operator $\left(Δ^τ \right)$, Schauder basis, infinite matrices and $α -,β-$ and $γ-$duals .

Toeplitz matrices for the study of the fractional Laplacian on a bounded interval

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…

On fractional Hadamard powers of positive block matrices

Entrywise powers of matrices have been well-studied in the literature, and have recently received renewed attention in the regularization of high-dimensional correlation matrices. In this paper, we study powers of positive semidefinite block matrices $(H_{st})_{s,t=1}^n$ with complex entries. We first characterize the powers $α\in\mathbb{R}$ such that the blockwise power map $(H_{st}) \mapsto (H_{st}^α)$ preserves Loewner positivity. The characterization is obtained by exploiting connections with the theory of matrix monotone functions developed by Loewner. Second, we revisit previous work by …

The Schur transformation for Nevanlinna functions: operator representations, resolvent matrices, and orthogonal polynomials

A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function $n$ with a suitable asymptotic expansion at $\infty$, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation $p$ times we find a Nevanlinna function $n_p$ which is a fractional linear transformation of the given function $n$. The main results concern the effect of this transformation to the realizations of $n$ an…