We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyze linear stability of the fundamental self-similar solution of the wave equation with a focusing power nonlinearity. This is Part 1 in a series of papers [Donninger, R., "Asymptotics and analytic modes for the wave equation in similarity coordinates," J. Evol. Equ. 9, 511 (2009); Donninger, R., " Nonlinear stability of self-similar solutions for semilinear wave equations," Commun. Partial Differ. Equ.]. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3299302]