This English edition is almost identical to the German original Lineare
Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in
1976. A few proofs have been simplified, some additional exercises have
been included, and a small number of new results has been added (e.g.,
Theorem 11.11 and Theorem 11.23). In addition a great number of minor
errors has been corrected. Frankfurt, January 1980 J. Weidmann vii
Preface to the German edition The purpose of this book is to give an
introduction to the theory of linear operators on Hilbert spaces and
then to proceed to the interesting applica- tions of differential
operators to mathematical physics. Besides the usual introductory
courses common to both mathematicians and physicists, only a fundamental
knowledge of complex analysis and of ordinary differential equations is
assumed. The most important results of Lebesgue integration theory, to
the extent that they are used in this book, are compiled with complete
proofs in Appendix A. I hope therefore that students from the fourth
semester on will be able to read this book without major difficulty.
However, it might also be of some interest and use to the teaching and
research mathematician or physicist, since among other things it makes
easily accessible several new results of the spectral theory of
differential operators.