Open AccessOn the Uniqueness of Inverse Eigenvalue Problems
Author(s) -
Barcilon Victor
Publication year - 1974
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1974.tb04121.x
Subject(s) - eigenvalues and eigenvectors , uniqueness , mathematical analysis , mathematics , inverse , inverse problem , boundary value problem , boundary (topology) , shear modulus , vibration , order (exchange) , uniqueness theorem for poisson's equation , differential equation , physics , geometry , thermodynamics , quantum mechanics , finance , economics
Summary The inverse eigenvalue problem consisting of the differential equation u (2 n ) ‐( p 1 u ( n ‐1) ) ( n ‐1) +…+(‐1) n p n u =Λ u together with suitable boundary conditions is examined. It is shown that n +1 spectra associated with n +1 distinct sets of boundary conditions are required in order to reconstruct the unknown coefficients p 1 , …, p n . The sixth order case is analogous to the eigenvalue problem for the spheroidal modes of vibrations of earth which have been used to infer the density, the bulk modulus and shear modulus.