Summary
The Schwinger and Kohn variational methods are derived in a unified manner from the approximation theory of linear operators in Hilbert space. The analytic basis behind their relationship with the method of the Padé approximants is clarified. The present formulation has enabled us to derive some known results in variational methods and the Padé approximants relatively briefly and simply.
Riassunto
Si sono dedotti in modo unificato i metodi variazionali di Schwinger e di Kohn dalla teoria di approssimazione degli operatori lineari nello spazio di Hilbert. Si è chiarita la base analitica che sottende il loro rapporto con il metodo degli approssimanti di Padé. Si è stati in grado con la presente formulazione di dedurre in modo relativamente breve e semplice alcuni risultati noti nei metodi variazionali e negli approssimanti di Padé.
Резюме
Из приближенной теории линейных операторов в Гильбертовом пространстве единым образом выводятся вариационные методы Швингера и Кона. Выясняется аналитическая осхова, определяющая связь этих вариационных методов с методом приближений Падэ. Предложенный формализм позволяет нам вывести некоторые известные результаты с помощью вариационных методов и приближений Падэ относительно быстро и просто.
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Singh, S.R., Stauffer, A.D. A unified formulation of the variational methods in scattering theory. Nuov Cim B 22, 139–152 (1974). https://doi.org/10.1007/BF02737466
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DOI: https://doi.org/10.1007/BF02737466