First, let me say that I think it would be easier to make suggestions if we had the entire sentence, because these sorts of suggestions are generally not "one size fits all." Also, if the sentences are short, changing them is much more difficult. For example:
There is too much debate about vaccines.
The only way to change that without adding information would be something like:
Too much debate about vaccines exists.
Vaccines are the subject of too much debate.
But that's not necessarily a better sentence than the original. Moving on to the next example, let's complete the sentence:
There are various views of the state of politics today.
One way to edit this is to provide a clear subject:
People have various views of the state of politics today.
The same is true for the next example:
It is believed that...
Provide a clear subject:
People believe that...
Some sentences can be changed to the passive voice (if your style allows for that):
There are many ways to represent functions.
Functions can be represented in many ways.
Considering that the first sentence doesn't have a clear subject, the change to the passive voice may not be such a bad thing.
Unfortunately, I don't have any references to back me up. My answers are based on 20+ years' experience as a copyeditor.