We report the results of our multi-wavelength observations of GRS 1758–258 made in August 1997 .
The energy bands include radio , millimeter , X-ray , and gamma-ray .
The observations enable us to obtain a complete spectrum of the source over an energy range of 2 – 500 keV .
The spectrum shows that GRS 1758–258 was in its hard state .
It is well fitted by the Sunyaev-Titarchuk ( ST ) Compton scattering model with a plasma temperature of 45 keV and a Thomson depth of 3.3 .
Taking relativistic effects into account , we get a little higher plasma temperature ( 52 keV ) by using the improved version of the ST model ( HT model ) plus a soft black-body component .
The spectrum is also fit by a power law with an exponential cutoff ( PLE ) plus a soft black-body component .
The temperature of the soft components in both models is about 1.2 keV , and the energy flux is less than 1.5 % of the total X- and gamma-ray flux .
The deduced hydrogen column density is in the range of ( 0.93 - 2.0 ) \times 10 ^ { 22 } cm ^ { -2 } .
No significant iron lines are detected .
The radio emission has a flat energy spectrum .
The daily radio , X-ray and gamma-ray light curves show that GRS 1758–258 was stable during the observation period , but was highly variable on smaller time scales in X- and gamma-rays .
The power density spectra are typical for the low-state , but we find the photon flux for the 5 to 10 keV band to be more variable than that in the other two energy bands ( 2 – 5 keV and 10 – 40 keV ) .
Harmonically spaced quasi-periodic oscillations ( QPOs ) are observed in the power spectra .
The phase lags between the hard photons and the soft photons have a flat distribution over a wide range of frequencies .
A high coherence of about 1.0 ( 0.01 – 1 Hz ) between the hard photons and the soft photons is also obtained in our observations .
We compare these results with two variation models .
Our millimeter observations did not reveal any conclusive signatures of an interaction between the jet from GRS 1758–258 and the molecular cloud that lies in the direction of GRS 1758–258 .