You might want to invest in a football display case with at least 50% UV protection. Sun light will do it's damage, even reflected sun light.
The Ideal conditions for display would be indirect lighting, at a room temperature of 65 - 70 degrees, and 50% humidity. Always check your signatures periodically for signs of fading or deterioration, and avoid excessive handling.
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There are many ways to authenticate a signed football, but many people take photo copies of the signature and then somehow market them back on the signed football.
To make sure an autographed football stays intact, it can be housed in a sealed box or case. You can also store it so it is protected from the elements.