The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator

Spectral analysis of tridiagonal Fibonacci Hamiltonians

We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.

Integer Powers of Certain Complex (2k+1)-diagonal Toeplitz Matrices

In this paper, we obtain a general expression for the entries of the lth (l is integer) powers of even order (2k+1)-diagonal Toeplitz matrices. Additionally, we have the complex factorizations of Fibonacci polynomials.

Bounds on the Spectral Sparsification of Symmetric and Off-Diagonal Nonnegative Real Matrices

We say that a square real matrix $M$ is \emph{off-diagonal nonnegative} if and only if all entries outside its diagonal are nonnegative real numbers. In this note we show that for any off-diagonal nonnegative symmetric matrix $M$, there exists a nonnegative symmetric matrix $\widehat{M}$ which is sparse and close in spectrum to $M$.

A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators

We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions $Ω\subseteq\real^N$, where the order $2m$ of the operator satisfies $N<2m$. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on $Ω$. Work of Barbatis is applied to find the best constant in this expression.

$S^1$-对称Kähler流形上部分Bergman核的非对角估计

Off-diagonal estimates of partial Bergman kernels on $S^1$-symmetric Kähler manifolds

本研究针对闭$S^1$-对称Kähler流形，建立了其上部分Bergman核的局部渐近估计，明确了一般非对角点处的标度渐近特性，并详细探讨了二维球面的对应情形。