Solution to the interior transmission problem using nodes on a subinterval as input data. (June 2017) - Yang, Chuan-Fu; Xu, Xiao-Chuan; Buterin, Sergey
Abstract: It is well known that a spherically symmetric wave speed problem in a bounded spherical region may be reduced, by means of Liouville transform, to the Sturm–Liouville problem B ( a ; q ) in [ 0, 1 ] . We prove that a twin dense subset of the nodal set in a subinterval ( ⊂ [ 0, 1 ] ) uniquely determines the potential q on the whole interval [ 0, 1 ] and the boundary parameter a . The method employed is to convert the inverse nodal problem into the inverse spectral problem with partial information given on the potential on a subinterval.