On the approximation of real powers of sparse, infinite, bounded and Hermitian matrices

Abstract

We describe a way to approximate the matrix elements of a real power $\alpha$ of a positive (for $\alpha \ge 0$) or non-negative (for $\alpha \in \mathbb{R}$), infinite, bounded, sparse and Hermitian matrix $W$. The approximation uses only a finite part of the matrix $W$.

9 pages; LaTeX; revised version (minor corrections); to appear in "Linear Algebra and its Applications"