In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition. Due to these changes, some theorems, lemmas, and formulas of the first edition are missing from the new edition while new ones are added.

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Biography of Tosio Kato

Tosio Kato was born in 1917 in a village to the north of Tokyo. He studied theoretical physics at the Imperial University of Tokyo. After several years of inactivity during World War II due to poor health, he joined the Faculty of Science at the University of Tokyo in 1951. From 1962 he was Professor of Mathematics at the University of California, Berkeley, where he is now Professor Emeritus.

Kato was a pioneer in modern mathematical physics. He worked in te areas of operator theory, quantum mechanics, hydrodynamics, and partial differential equations, both linear and nonlinear.

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