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Partial inverse problems for quadratic differential pencils on a graph with a loop

Partial inverse problems for quadratic differential pencils on a graph with a loop

Abstract In this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the …