[share_ebook] Linear Operators Part III: Spectral Operators (Pure & Applied Mathematics, Volume 7, Part 3) (v. 3)

In presenting the theory of spectral operators in Part III, we had to cope with two independent problems of exposition not encountered in the first two parts. We briefly describe these problems here, for such a discussion gives the reader a historical perspective of Part III, as well as that of the treatise as a whole, and shows him where the existing mathematical theory, and its close relations to certain profound empirical results of contemporary physics, verges on the boundary between the known and the unknown. The applications to physics involve not only problems emerging from recent theories such as quantum mechanics, scattering theory, quantum field theory, and the quantum mechanical version of the three body problem, but also nonselfadjoint problems arising from more classical problems such as a large variety of diffusion phenomena, and particularly electromagnetic wave theory. We present the abstract operator theory in the text, and then in the Notes and Remarks, especially in Section XX.6, give the physical interpretations as well as a brief discussion of past and present related problems.