Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Discrete Hausdorff Transformations

Gerald Leibowitz
Proceedings of the American Mathematical Society
Vol. 38, No. 3 (May, 1973), pp. 541-544
DOI: 10.2307/2038946
Stable URL: http://www.jstor.org/stable/2038946
Page Count: 4
Let K be a complex valued measurable function on (0, 1\rbrack such that $\int^1_0 t^{-1/p}| K(t)| dt$ is finite for some $p > 1$. Let H be the Hausdorff operator on lp determined by the moments μn = ∫1 0 tnK(t)dt. Define Ψ(z) = ∫1 0 tzK(t)dt. Then for each z with $\operatorname{Re} z > -1/p, \Psi(z)$ is an eigenvalue of H*. The spectrum of H is the union of $\{0 \}$ with the range of Ψ on the half-plane ℜ z ≥ -1/p.