We consider the prospects for detecting solar-like oscillations in the
"super-Nyquist" regime of long-cadence (LC) Kepler photometry, i.e., above the
associated Nyquist frequency of approximately 283 {\mu}Hz. Targets of interest
are cool, evolved subgiants and stars lying at the base of the red-giant
branch. These stars would ordinarily be studied using the short-cadence (SC)
data, since the associated SC Nyquist frequency lies well above the frequencies
of the detectable oscillations. However, the number of available SC target
slots is quite limited. This imposes a severe restriction on the size of the
ensemble available for SC asteroseismic study.We find that archival Kepler LC
data from the nominal Mission may be utilized for asteroseismic studies of
targets whose dominant oscillation frequencies lie as high as approximately 500
{\mu}Hz, i.e., about 1.75- times the LC Nyquist frequency. The frequency
detection threshold for the shorter-duration science campaigns of the
re-purposed Kepler Mission, K2, is lower. The maximum threshold will probably
lie somewhere between approximately 400 and 450 {\mu}Hz. The potential to
exploit the archival Kepler and K2 LC data in this manner opens the door to
increasing significantly the number of subgiant and low-luminosity red-giant
targets amenable to asteroseismic analysis, overcoming target limitations
imposed by the small number of SC slots.We estimate that around 400 such
targets are now available for study in the Kepler LC archive. That number could
potentially be a lot higher for K2, since there will be a new target list for
each of its campaigns.Comment: Accepted for publication in MNRAS; 11 pages, 7 figures; reference
list update