It's called an "inverter" air conditioner. It produces a variable-frequency AC sine wave from the DC voltage. The variable-frequency to the compressor changes the cooling output, so instead of turning the air conditioner on and off as the temperature wanders back and forth across the set point, it varies the frequency to keep the temperature steady.
It is brilliant.
Sharp already sells these air conditioners. They're just removing the DC rectifier circuit and running directly on DC instead of starting with 50hz or 60hz AC.