We discuss a series of observations of the black hole candidate GX 339-4 in low luminosity, spectrally hard states. We present spectral analysis of three separate archival Advanced Satellite for Cosmology and Astrophysics (ASCA) data sets and eight separate Rossi X-ray Timing Explorer (RXTE) data sets. Three of the RXTE observations were strictly simultaneous with 843 MHz and 8.3-9.1 GHz radio observations. All of these observations have (3-9 keV) flux approximately < 10^{-9} ergs s^{-1} cm^{-2}. The ASCA data show evidence for an 6.4 keV Fe line with equivalent width 40 eV, as well as evidence for a soft excess that is well-modeled by a power law plus a multicolor blackbody spectrum with peak temperature 150-200 eV. The RXTE data sets also show evidence of an Fe line with equivalent widths 20-140 eV. Reflection models show a hardening of the RXTE spectra with decreasing X-ray flux; however, these models do not exhibit evidence of a correlation between the photon index of the incident power law flux and the solid angle subtended by the reflector. `Sphere+disk Comptonization models and Advection Dominated Accretion Flow (ADAF) models also provide reasonable descriptions of the RXTE data. The former models yield coronal temperatures in the range 20-50 keV and optical depths of tau ~ 3. The model fits to the X-ray data, however, do not simultaneously explain the observed radio properties. The most likely source of the radio flux is synchrotron emission from an extended outflow of size greater than O(10^7 GM/c^2).
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