With rare exceptions, nobody reads dissertations except the author and his or her committee. But people might read papers that come out of dissertations.
Credibility radiates outward from one's research topic. If you write a dissertation on Peruvian tree frogs, then you're an expert on Peruvian tree frogs. But you probably know something about Peru and something about other kinds of tree frogs. And presumably you know basic biology pretty well.
A PhD in any math topic implies credibility in math. However, you may want to help the reader see that. The dissertation or paper title may be so full of jargon that a non-expert may not be able to tell what general area of math it's in, or even that it's in math.
For example, my dissertation was something like "Microstructure models with secondary flux". What's that? Physics? Engineering? Math? What kind of math? So I might explain that I looked at partial differential equation models applied to fluid flow.
