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Spectral theory of operators in Hilbert space

Author: K O Friedrichs
Publisher: New York : Springer-Verlag, 1980.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 9.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. Next, simple differential operators are treated  Read more...

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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: K O Friedrichs
ISBN: 0387900764 9780387900766 3540900764 9783540900764
OCLC Number: 10416863
Notes: 2nd, corrected printing.
Originally published: 1973.
Index: p. 242-244.
Description: viii, 244 pages ; 25 cm.
Contents: 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.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 9.
Responsibility: K.O. Friedrichs.

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