"Specialize" as a transitive verb and an antonym for "generalize"

In mathematical writing, I would like to find a transitive verb that means to "apply a general theory to a special case in order to get a theory for this special case". In other words, it should be an antonym for "generalize" when it means to "make a theory widely applicable". For example,

"One of the most important branches of mathematics is the study of objects known as manifolds, which results from generalizing these ideas to three or more dimensions."

"Caution should be used in generalizing this study’s results to other student populations."

I wanted to use "specialize". For example,

"We specialize this theorem to the case that …"

Here is more or less the real situation. We have a theory that concerns a sequence of functions {f_k} and a sequence of matrices {M_k}. In the theory, under assumption A({f_k}, {M_k}), we have conclusion C({f_k}, {M_k}). This is our general theory. Meanwhile, we have another sequence of functions {F_k} and a sequences of vectors {v_k}; defining f_k = f(F_k, v_k) and M_k=M(F_k, v_k), and apply the aforementioned theory to this special configuration of {f_k} and {M_k}, we get our special theory. In this process, we do nothing but expressing A({f_k}, {M_k}) and C({f_k}, {M_k}) in terms of {F_k} and {v_k} (with reformulations and simplifications).

However, "specialize" seems to be only an intransitive verb, and it means to concentrate on and become an expert in a particular subject or skill. For example, see

https://www.oxfordlearnersdictionaries.com/definition/english/specialize?q=specialize,
https://www.lexico.com/definition/specialize ,
https://dictionary.cambridge.org/dictionary/english/specialize ,
and
https://www.ldoceonline.com/dictionary/specialize .

Fortunately, in the 2nd item of
https://www.oed.com/view/Entry/185980?redirectedFrom=specialize#eid ,
"specialize" can mean "to make special, specific, or narrower in scope; to invest with a special character or function", which is what I want. But it is mentioned to be "now somewhat rare", which explains why this meaning is not mentioned in the aforementioned dictionaries.

Question:

1. What is the best word to work as the antonym of "generalize" in the above-mentioned scenario?

2. Is it good to use "specialize" as a transitive verb in this scenario?

3. (new) Is "particularize" of "specify" a good choice?

Any comments or criticism will be highly appreciated. Thank you very much.