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เนื้อหาย่อ : ABOUT THIS VOLUME In this up-to-date account the author brings together the recent developments in multiparameter spectral theory in Hilbert space. The theory of linear operators in tensor products of Hilbert spaces is described, and a multiparameter spectral theory for both bounded and unbounded operators developed. The main results of the book are illustrated by application to systems of linked ordinary differential equations, completely coupled systems of operator equations and polynomial bundles. A concluding review of the current state of the subject points the way to further research. This account will be of value to theoretical physicists and mathematicians with a particular interest in spectral theory and differential equations. RESEARCH NOTES IN MATHEMATICS The aim of this series is to disseminate important new material of a specialist nature in econornic form. It ranges over the whole spectrum of mathematics and also reflects the changing mo mentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline. The editorial board has been chosen accordingly and will from time to time be recomposed to represent the fuli diversity of mathematics as covered by Mathematical Reviews. This is a rapid : neans of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph, will also be considered for a place in the series. Normally homogeneous material is required, even if written by more than one author, thus multi-author works will be included provided that there is a strong linking theme or editorial pattern. Proposals and manuscripts: See inside back cover.