  The thermal fluctuation spectrum of a fluid membrane coupled harmonically to
a solid support by an array of tethers is calculated. For strong tethers, this
spectrum exhibits non-monotonic, anisotropic behavior with a relative maximum
at a wavelength about twice the tether distance. The root mean square
displacement is evaluated to estimate typical membrane displacements. Possible
applications cover pillar-supported or polymer-tethered membranes.
