When the domain satisfies , then a solution comes from Operator theory as follows.

Set

for

and

for .

It is not hard to see that for all .

And thus , which implies that and that has the inverse operator .

Rewritting the given equation, we have

, which gives .

On the other hand, implies , and therefore .

However, this method does not help when the domain is a superset of the interval .

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