Linear Operators in Hilbert Spaces

1. Front Matter

   Pages i-xiii

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2. Vector spaces with a scalar product, pre-Hilbert spaces

   • Joachim Weidmann

   Pages 1-14

3. Hilbert spaces

   • Joachim Weidmann

   Pages 15-28

4. Orthogonality

   • Joachim Weidmann

   Pages 29-49

5. Linear operators and their adjoints

   • Joachim Weidmann

   Pages 50-87

6. Closed linear operators

   • Joachim Weidmann

   Pages 88-128

7. Special classes of linear operators

   • Joachim Weidmann

   Pages 129-165

8. The spectral theory of self-adjoint and normal operators

   • Joachim Weidmann

   Pages 166-228

9. Self-adjoint extensions of symmetric operators

   • Joachim Weidmann

   Pages 229-268

10. Perturbation theory for self-adjoint operators

    • Joachim Weidmann

    Pages 269-288

11. Differential operators on L 2(ℝm)

    • Joachim Weidmann

    Pages 289-336

12. Scattering theory

    • Joachim Weidmann

    Pages 337-361

13. Back Matter

    Pages 362-402

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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.

• Hilbert space
• Hilbertscher Raum
• Koordinatentransformation
• Lebesgue integration
• Operators
• complex analysis
• convergence
• differential equation
• integral
• integration
• linearer Operator
• operator
• ordinary differential equation
• schrödinger operator
• spectral theorem

• Institut für Angewandte Mathematik, Mathematisches Seminar der Johann-Wolfgang-Goethe-Universität, 6 Frankfurt a. M., Federal Republic of Germany

  Joachim Weidmann