Is there any difference between the two sentences?
1. Carl Sagan served as the David Duncan Professor of Astronomy and Space Sciences at Cornell University.
2. Carl Sagan served as David Duncan Professor of Astronomy and Space Sciences at Cornell University.
I don't think that there are two David Duncan chairs in the said university.
My sentence is a modified quotation from Carl Sagan's famous book entitled COSMOS. Is there any likelihood that the sentence given in the book is wrong? In so far as I know, when there is only one post we do not use the definite article as in "Derrida was appointed Professor of the Humanities at the University of California". Another:
Hawking is Lucasian Professor of Mathematics at the University of Cambridge.
I would like to know whether Ameircan and British usages differ in this regard.
Firstly, you do not "serve" as a professor. You are the xxxx Professor.
You say you have modified Sagan's own sentence? I rather feel he can be counted on having the correct terms.
Carl Sagan was David Duncan Professor of Astronomy and Space Sciences at Cornell University is correct terminology. It is his academic title.
Another way of phrasing it, where the is required would be "The David Duncan ... at Cornell University in the years xxxx to xxxx was Carl Sagan".
For your reading I reproduce in full the text of what is written on the inside cover of Carl Sagan's book COSMOS.
Carl Sagan served as the David Duncan Professor of Astronony and Space Sciences and Director of the Laboratory for Planetary Studies at Cornell University. He played a leading role in the Mariner,Viking,Voyager,and Galileo Spacecraft expeditions to the planets for which he received the NASA Medals for Exceptional Scientific Achievement and (twice) for Distinguished Public Service.