Spectral Theory of Self-Adjoint Operators in Hilbert Space

1. Front Matter

   Pages i-xvi

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2. Preliminaries

   • M. S. Birman, M. Z. Solomjak

   Pages 1-17

3. Hilbert Space Geometry. Continuous Linear Operators

   • M. S. Birman, M. Z. Solomjak

   Pages 18-59

4. Unbounded Linear Operators

   • M. S. Birman, M. Z. Solomjak

   Pages 60-96

5. Symmetric and Isometric Operators

   • M. S. Birman, M. Z. Solomjak

   Pages 97-122

6. Spectral Measure. Integration

   • M. S. Birman, M. Z. Solomjak

   Pages 123-139

7. Spectral Resolutions

   • M. S. Birman, M. Z. Solomjak

   Pages 140-158

8. Functional Model and the Unitary Invariants of Self-adjoint Operators

   • M. S. Birman, M. Z. Solomjak

   Pages 159-182

9. Some Applications of Spectral Theory

   • M. S. Birman, M. Z. Solomjak

   Pages 183-205

10. Perturbation Theory

    • M. S. Birman, M. Z. Solomjak

    Pages 206-220

11. Semibounded Operators and Forms

    • M. S. Birman, M. Z. Solomjak

    Pages 221-241

12. Classes of Compact Operators

    • M. S. Birman, M. Z. Solomjak

    Pages 242-278

13. Commutation Relations of Quantum Mechanics

    • M. S. Birman, M. Z. Solomjak

    Pages 279-296

14. Back Matter

    Pages 297-301

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It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com­ pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non­ trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

• Hilbert space
• convergence
• differential equation
• filtering
• integrable system
• integral
• integration
• measure
• measure theory
• metric space
• operator
• schrödinger operator
• spectral theorem

• Department of Physics, Leningrad University, U.S.S.R.

  M. S. Birman

• Department of Mathematics, Leningrad University, U.S.S.R.

  M. Z. Solomjak

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