دانلود کتاب PT-Symmetric Schrödinger Operators with Unbounded Potentials

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Cover......Page 1
PT-Symmetric Schrödinger Operators with Unbounded Potentials......Page 4
ISBN 9783834817624......Page 5
Acknowledgment......Page 6
Table of Contents......Page 8
Introduction......Page 10
1.1 Linear Operators in Krein Spaces......Page 18
1.2.1 Relatively Bounded and Relatively CompactOperators......Page 23
1.2.2 The Case of Relative Bound 0......Page 26
1.2.3 Stability of Self-Adjointness in Krein Spaces......Page 28
1.3.1 Continuity of Resolvents......Page 29
1.3.2 Perturbation of Isolated Parts of the Spectrum......Page 32
1.3.3 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces......Page 35
1.3.4 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces......Page 39
2.1.1 Accretive and Sectorial Operators......Page 44
2.1.2 Quadratic Forms and Associated Operators......Page 45
2.1.3 Relatively Form-Bounded andRelatively Form-Compact Operators......Page 51
2.2 Continuity of Separated Parts of theSpectrum......Page 55
2.2.1 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces......Page 56
2.2.2 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces......Page 62
2.3.1 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces......Page 68
3.1 Example 1......Page 74
3.2 Example 2......Page 78
3.3 A Class of Schrödinger Operators withRelatively Bounded Complex Potentialsand Real Spectrum......Page 81
Bibliography......Page 88