How to find people who do similar research? I am 28 years old and did my PhD last year at an applied math institute and left. However, I am still in good contact with my old working group  and my PhD adviser told me I should come back.

At the moment I am a self-employed programmer. Although I really like my current job, I sometimes wonder if I should give the academic career another try. The main reason why I left was that I did not feel integrated in research society.

To be more precise, most articles I read where between 1950-1960. Most of my focus area are was out of scope from my adviser (he is an expert in numerical optimization, I was doing measure theory and Markov operator theory combined with numerical optimization). I had a lot of fun to modernize old theorems and try to apply them to numeric problems. Although I enjoyed the freedom of doing research on my own, I often was wondering if the results that I found are already known. My advisor was often surprised about my fundamental results, but he could not tell me if they are actual new. In fact, after searching persistent for one of my main theorems, I found it in a booklet from 1960 written with a typewriter - with a much shorter and genial proof.  Although most of my other theorems have been peer-reviewed and published in B journals, I am still waiting for someone contacting me: "Hello, your result X in journal Y is known for a long time".

The author of this typewritten book is actually still alive (85 years old), on facebook and on top of that even accepted my friend-request. However, lives in New York and I live in Germany, so I can't easily visit for a short talk. I did send a text message, but  never received a reply, I am not sure if it was because they do not want to talk about math anymore or if they just did not receive it, because facebook sometimes hides messages.

I was searching the web for professors doing similar research to what I am interested (by entering some keywords together with university into google). However, when I scanned their recent publications, I had no idea what they are doing. 

I think I might missed the opportunity to connect to other working groups. I love teaching and doing research, but I also hate doing isolated research and having no defined task.

Is there any specific way of finding people who do similar research that I am not aware of?
MathSciNet is a pretty powerful tool for finding things in math, and some parts of applied math (from the question, I think it cover your areas).  (There's also Zentralblatt--I'm less familiar with that, but I think MSN will have more relevant tools for you.)  See about getting access to that as a guest at a local university.  

Then here are some things you can do:


Starting with papers you know that are close to your area, look them up in MathSciNet and look at the papers citing them or citing their reviews (of course you can do the first with Google scholar also, for papers that are available online).  Read the reviews to see if they are of interest.  For the ones that look interesting, repeat.  You can similarly look up all publications by a given author.
You can also search in MathSciNet by Math. Subject Classification codes to look for papers in certain subareas of applied math.
Without MathSciNet access, you can search for things on the arXiv or Google Scholar with keywords/authors/etc.  I guess this is what you have been doing.  Note, unlike Google Scholar, arXiv has subject classifications and anyone can read any paper listed there.
The subject has probably advanced a lot in 50-60 years, so it's may not be strange if most of the stuff going on now doesn't seem (at least on the surface) too close to the papers you were reading from the '50s and '60s.  So you might try looking for and reading some survey papers/lecture notes/textbooks to get a better sense of the area first.
If possible, try going to some conferences/local seminars and talking to people.