Non-self-adjoint Schrödinger operator with a periodic potential / / Oktay Veliev

• Record Nr.: UNINA9910485598603321
• Autore: Veliev Oktay
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-72683-5
• Descrizione fisica: 1 online resource (301 pages)
• Disciplina: 515.724
• Soggetti: Schrödinger operator
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction and Overview -- 2 Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential -- 2.1 Introduction -- 2.2 On the Floquet Theory and Spectrum of L(q) -- 2.3 Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- 2.3.1 Uniform Asymptotic Formulas for the Isolated Eigenvalues -- 2.3.2 Asymptotic Formulas for the Isolated Pairs -- 2.3.3 On the Numerations of the Bloch Eigenvalues and Bands -- 2.4 Spectral Singularities and ESS of the Operator L(q) -- 2.5 Spectral Expansion for the Non-self-adjoint Operator L(q) -- 2.6 The Necessity of the Brackets and P.V. Integrals and Criteria for the Elegant Expansion -- 2.7 On the Asymptotic Spectrality of L(q) -- 2.7.1 Spectral Singularities and Spectrality -- 2.7.2 On the Asymptotically Spectral Potentials -- 2.8 Appendices -- 3 On the Special Potentials -- 3.1 On the Even Potentials -- 3.2 On the PT-Symmetric Potentials -- 3.2.1 General Properties of the Spectrum -- 3.2.2 On the Bands Γn for Large n -- 3.2.3 Reality and Non-Reality of the Bands and Spectrality of L(q) -- 3.2.4 Finite Zone PT-Symmetric Periodic Potentials -- 3.2.5 Conclusions, Notes and References -- 3.3 Pure Complex-Valued Potentials with Pure Real Spectrum -- 3.3.1 On the Bloch Eigenvalues and Bloch Function -- 3.3.2 On the Inverse Problem -- 3.3.3 On the Spectral Singularities and ESS -- 4 On the Mathieu-Schrödinger Operator -- 4.1 Introduction -- 4.2 Asymptotic Formulas for the Isolated Eigenvalues and Isospectrality -- 4.3 Asymptotic Formulas for ; the Pairs of the Eigenvalues and Spectrality -- 4.4 On the ESS and Spectral Expansion of H(a,b) -- 4.5 On Simplicity of the Periodic and Antiperiodic Eigenvalues and Elegant Spectral Expansion -- 5 PT-Symmetric Periodic Optical Potential -- 5.1 Introduction -- 5.2 On the Bloch Eigenvalues.; 5.3 On the Bands and Components of the Spectrum -- 5.4 Spectral Singularities, ESS and Spectral Expansion -- 5.5 Finding the Second Critical Point -- 5.6 On the Small Perturbations -- 5.7 Conclusions and Notes -- Index.