Spectral Theory of Operators in Hilbert Space (Applied Mathematical Sciences, 9)

Friedrichs, Kurt O.

ISBN 10: 0387900764 / ISBN 13: 9780387900766

Editore: Springer, 1981

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Codice articolo ERICA77303879007646

Dati bibliografici

• Titolo: Spectral Theory of Operators in Hilbert Space (Applied Mathematical Sciences, 9)
• Editore: Springer
• Data di pubblicazione: 1981
• Lingua: Inglese
• ISBN 10: 0387900764
• ISBN 13: 9780387900766
• Rilegatura: Paperback
• Condizione: Very Good
• Tipo di libro: book

Descrizione articolo

Riassunto

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 as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra.

Contenuti

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.