ON THE SPECTRAL PROPERTIES OF A WAVE OPERATOR PERTURBED BY A LOWER-ORDER TERM - A.Sh.Shaldanbayev; M.I.Akylbayev; A.A.Shaldanbayeva; A.Zh.Beisebayeva (Academic Scientific Journal of Computer Science, 2019)
The incorrectness of the minimal wave operator is well known, since zero is an infinite-to-one eigenvalue for it. As our study showed, the situation changes if the operator is perturbed by a low-order term containing the spectral parameter as a coefficient, and eventually the problem takes the form of a beam of operators. The resulting beam of operators is easily factorized by first-order functional-differential operators which spectral properties are easily studied by the classical method of separation of variables. Direct application of the method of separation of variables to the original beam of operators encounters the insurmountable difficulties.