Ambarzumyan, Ivanenko and the inverse Sturm - Liouville problem

I have seen a recent article: arXiv: 1301.3276, devoted to the pioneer work of Victor Ambarzumyan on the Sturm – Liouville inverse problem in 1929 (Zeitschrift f\"ur Physik, 53, 690-695). It is interesting that an idea of this work belongs to Dmitri Ivanenko, as it follows from the letter of Ambarzumyan to Ivanenko in connection with Ivanenko’s 60s jubilee in 1964. The letter is in Russian, and I provide the English translation of this part.

"In one of our discussions, you posed a question on the uniqueness of definition of a mechanical system by the spectrum of its eigenvalues. It motivated me to write my first article of 1929 on the inverse Sturm – Liouvolle problem. After that, many authoritative mathematicians devoted their attempts to this problem. If today some of them mention my work, then I in turn give you thanks for that discussion which occurred in 1928."