If I have implemented a Java Library (that offers certain functionality), could I transform this into a JavaScript library, such that the same functionality can be offered? I know this may be an ask, but, I was wondering if there are frameworks existing that help in this?
No, in general this is not possible, Java and JavaScript are more or less completely different languages.
However there are a couple of Java to JavaScript translators that you can try. Java2Script is one such tool. Apparently the Google Web Toolkit (GWT) does this as well. Source.
While you could probably do some sort of conversion, it's important to note that Java and JavaScript, while similarly named, are not at all related. Unfortunately, I think you'll be hard pressed to find a framework or system that does a good job converting one to the other. :(
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