Chosen Solution

Can I run 350 RMS (500 PEAK) amplifier for 350RMS (1300 WATT) subwoofer ?

The short answer is yes. The longer is that the system won’t sound as it should. Basically, the ratings on a speaker system indicate not only the max power, but also what the speaker wants in order to perform to specs. You can always use a speaker rated for a higher wattage with an amp that has less, except that the amp will be at max most of the time when you want volume. For a speaker that can handle 800 watts, I would want an amp that delivers around 1000W. This means that you can run the amp at 80% (which is a good point) and get full performance out of the speaker. Also realize that there is a difference between peak and sustained power capability. If the speaker is rated at 800W continuous, do NOT drive it with more than that for an extended period of time. If you do, you will damage the speaker. Dan