  (Abridged) We present an analysis of the X-ray spectrum of the Galactic
shell-type supernova remnant (SNR) G347.3-0.5 (RX J1713.7-3946). By performing
a joint spectral analysis of data from observations made of G347.3-0.5 using
the ROSAT PSPC, the ASCA GIS and the RXTE PCA, we have fit the spectra of
particular regions of this SNR (including the bright northwestern and
southwestern rims, the northeastern rim and the interior diffuse emission) over
the approximate energy range of 0.5 through 30 keV. Based on the parameters of
the best fit to the spectra using the SRCUT model, we estimate the maximum
energy of cosmic-ray electrons accelerated by the rims of G347.3-0.5 to be
19-25 TeV, assuming a magnetic field strength of 10 microGauss. We present a
broadband (radio to gamma-ray) photon energy flux-spectrum for the northwestern
rim of the SNR, using a synchrotron-inverse Compton model with a variable
magnetic field strength to fit the spectrum. Our fit derived from this model
yields a maximum energy of only 8.8 TeV for the accelerated cosmic-ray
electrons and a magnetic field strength of 150 microGauss. However, our derived
ratio of volumes for TeV emission and X-ray emission (approximately 1000) is
too large to be physically acceptable. We argue that neither non-thermal
bremsstrahlung nor neutral pion decay can adequately describe the TeV emission
from this rim, and therefore the physical process responsible for this emission
is currently uncertain. Finally, we compare the gross properties of G347.3-0.5
with other SNRs known to possess X-ray spectra dominated by non-thermal
emission.
