Is this endgame position winning?

I assumed so entering it and felt confident during. My opponent blundered, but before that I was starting to wonder how to break through.

I suppose a good idea was to go after the a pawn which only the king can defend. With your dark squared bishop you could put pressure on other pawns like the f pawn. Another thing you could do, is to try to capture the c4 pawn, and you will be up a pawn. You could do this by first going for the a pawn and then plave your bishop and lastly bring your king in the attack. I don't know if you could think of all this in a blitz game, but in a classical you might could.

I think black can defend it. The center is inaccessible. If you try to march to a6, then black marches there first. If you try to march to h4 then black goes to g6.

If you try that immediately you might be right but I mention some general ideas on how you could win this endgame.

I believe it is unwinnable. Black can defend against whatever you try. The doubled pawns are a dynamic liability i.e. they are difficult to advance, but they are a static asset i.e. they are very good at staying where they are and denying white access to squares.

Looks drawn. No way to enter the black position

Thanks