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%Lower bounds Abstract for summability day, Chicago, 2006

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{\textbf{Hausdorff Prime Matrices}} \vskip .25in

{\textbf{Billy Rhoades}}\vskip .25in

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In 1933 Hille and Tamarkin proved that every Hausdorff matrix with
moment generating function $f(z) = {(z - a)/(z + 1)}$, $\Re(a) >
0$ is prime and raised the question of whether or nor each prime
is of this form.  My talk will answer this question.

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Hausdorff matrices form a class of infinite lower triangular
matrices with many nice algebraic properties.  In this expository
talk I will examine the basic properties of these matrices, and
mention  results of some of the contributors to this field of
study, which include (in alphabetical order): R. P. Agnew, G.
Bennett, S. K. Basu, H. L. Garabedian, G. H. Hardy, E. Hille, B.
Kuttner, M. S. Paramaswaran, B. E. Rhoades, and H. S. Wall.
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