In the Scrum Guide it is indicated that each Scrum Team must have its Product Owner and that the Product Backlog is unique per product. However, if several development teams work on the construction of a single product, it is clear that the Product Backlog will be common to all of them but what is not so clear is whether there is a single Product Owner.
For example, in questions like the following the idea of a single Product Owner is considered correct: To deliver to single product, three different Development teams are formed. How many product owners are needed?
Scrum says PO can cater to one or more teams though each team should has it's own PO means a team should not be interacting with multiple POs while a PO can interact with multiple teams & in essence this quite fair a real day to day scenario.
I hope now you get what Scrum recommends on PO. one PO for multiple teams :)