Algorithms for Calculating Eigen Values of Differential Operators with Unsmooth Potential on A Projective Plane
The modeling of various processes in natural and engineering sciences in some cases leads to problems of finding the eigenvalues of operators. The problems of the hydrodynamic theory of stability, electric oscillations in a long line, seismic prospecting, problems of non-destructive testing, image processing, composite materials identification, etc. are a good example. The solving of a wide range of natural science problems which involves finding eigenvalues of differential operators with complex spectral parameter, as a rule, means finding asymptotic formulas. The latter, in turn, seriously complicates the process of obtaining the desired result. The addition theorem allows to circumvent these difficulties in the case of considering operators with a unsmooth potential on the projective plane. On its basis, some fairly effective algorithms for calculating perturbation theory corrections have been developed.