Titchmarsh Е.С. Eigenfunction expansions associated with second-order differential equations. Part Two

Second ed. — Oxford: Clarendon Press, 1970. — 404 p.In Part One a theory of eigenfunction expansions associated with ordinary second-order differential equations was given. Here a similar theory is constructed for partial differential equations of the second order. It starts from the case of a rectangle with potential-function zero (ordinary multiple Fourier series), and is extended by limiting processes to general second- order equations in the whole space. Theorems on the nature of the spectrum, the distribution of the eigenvalues, and the convergence or summability of the eigenfunction expansion are proved. There follow chapters on perturbation theory (involving both discrete and continuous spectra) and on the case where the potential function is periodic. In the last chapter theorems in general analysis which are quoted in the main text are proved.
Перевод на русский язык. Титчмарш Э.Ч. Разложения по собственным функциям, связанные с дифференциальными уравнениями второго порядка. Том 2. /file/386499/