I overheard my coworker (entry-level but very intelligent and articulate), "Jane", tell a group of my peers that she thought I was unqualified to be a senior developer in our team.

I strongly believe that there should be a healthy level of trust and mutual respect among teammates for maximum team efficiency. Unfortunately, those key ingredients are now missing between us, and I'm concerned that this can negatively affect our success in an upcoming project that I've been assigned to lead (and where Jane is a junior developer).

How do I resolve this "issue" between Jane and me so that we could work together effectively?