On Inverse Scattering on a Sun-Type Graph

A partial inverse Sturm‐Liouville problem on an arbitrary graph

“…For a complex sequence { n } ∞ n=1 with only finite multiplicities, define I and {m n } n ∈ I by (17). Without loss of generality we assume that n = n+1 = … = n+m n −1 for all n ∈ I.…”

“…Inverse problems for differential operators on graphs appeared to be significantly more difficult for investigation because of complex structure of such operators. Various approaches to inverse problems for quantum graphs were developed in papers [9][10][11][12][13][14][15][16][17] and other studies. For recovering coefficients of differential operators on graphs, usually a large amount of spectral data is needed.…”

Spectral analysis of the Sturm‐Liouville operator on the star‐shaped graph

“…Relying on that method, Yurko and other mathematicians have solved inverse spectral problems for differential operators on arbitrary compact graphs (see [29]) and inverse spectral-scattering problems on noncompact graphs (see [27][28][29]). There were also attempts to apply the methods of Marchenko (see [33,37]) to inverse scattering problems for special types of graphs with infinite rays (see [11,17,31,32]). Nevertheless, although there is a significant number of studies on inverse problems for differential operators on graphs, they concern only uniqueness theorems and constructive algorithms for solution.…”

An inverse problem for an integro‐differential operator on a star‐shaped graph

“…Classical results of the inverse spectral theory are presented, e.g., in the monographs [13][14][15][16]. IPs for differential operators on graphs with local MCs were studied in [17][18][19][20][21][22][23][24][25] and other papers. Methods for solving inverse spectral problems for differential operators with nonlocal integral BCs on finite intervals were developed by Kravchenko [26], Yang and Yurko [27][28][29].…”