Author | Friedrichs, K. O. author |
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Title | Spectral Theory of Operators in Hilbert Space [electronic resource] / by K. O. Friedrichs |
Imprint | New York, NY : Springer New York, 1973 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6396-8 |
Descript | IX, 245 p. online resource |
I. Spectral Representation -- 1. Three typical problems -- 2. Linear space and functional representation. Linear operators -- 3. Spectral representation -- 4. Functional calculus -- 5. Differential equations -- II. Norm and Inner Product -- 6. Normed spaces -- 7. Inner product -- 8. Inner products in function spaces -- 9. Formally self-adjoint operators -- 10. Adjoint operators in function spaces -- 11. Orthogonality -- 12. Orthogonal projection -- 13. Remarks about the role of self-adjoint operators in physics -- III. Hilbert Space -- 14. Completeness -- 15. First extension theorem. Ideal functions -- 16. Fourier transformation -- 17. The projection theorem -- 18. Bounded forms -- IV. Bounded Operators -- 19. Operator inequalities, operator norm, operator convergence -- 20. Integral operators -- 21. Functions of bounded operators -- 22. Spectral representation -- 23. Normal and unitary operators -- V. Operators with Discrete Spectra -- 24. Operators with partly discrete spectra -- 25. Completely continuous operators -- 26. Completely continuous integral operators -- 27. Maximum-minimum properties of eigenvalues -- VI. Non-Bounded Operators -- 28. Closure and adjointness -- 29. Closed forms -- 30. Spectral resolution of self-adjoint operators -- 31. Closeable forms -- VII. Differential Operators -- 32. Regular differential operators -- 33. Ordinary differential operators in a semi-bounded domain -- 34. Partial differential operators -- 35. Partial differential operators with boundary conditions -- 36. Partial differential operators with discrete spectra -- VIII. Perturbation of Spectra -- 37. Perturbation of discrete spectra -- 38. Perturbation of continuous spectra -- 39. Scattering -- References