Locke J. Eigenvalues and completeness for regular and simply irregular two-point differential operators. - Providence: American Mathematical Society, 2008. - vii, 177 p. - (Memoirs of the American Mathematical Society; Vol.195, N 911). - Bibliogr.: p.171-173. - Ind.: p.175-177. - ISBN 978-0-8218-4171-6; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Chapter 1. Introduction ......................................... 1 1.1. Definitions and Notations .............................. 1 1.2. Summary of Results ..................................... 3 Chapter 2. Birkhoff Approximate Solutions ...................... 13 2.1. Birkhoff Approximate Solutions ........................ 13 2.2. Special Case: n = 2 ................................... 18 Chapter 3. The Approximate Characteristic Determinant: Classification ...................................... 19 3.1. The Approximate Characteristic Determinant ............ 19 3.2. Classification for n Even ............................. 23 3.3. Classification for n Odd .............................. 31 Chapter 4. Asymptotic Expansion of Solutions ................... 39 4.1. Expansions for n Even ................................. 39 4.2. Expansions for n Odd .................................. 50 Chapter 5. The Characteristic Determinant ...................... 57 5.1. The Characteristic Determinant for n Even ............. 57 5.2. The Characteristic Determinant for n Odd .............. 66 5.3. Special Case: n = 2 ................................... 70 Chapter 6. The Green's Function ................................ 75 6.1. The Green's Function for n Even ....................... 75 6.2. The Green's Function for n Odd ........................ 87 Chapter 7. The Eigenvalues for n Even .......................... 99 7.1. Case 1. p = q, ξ0 ≠ η0 ............................... 104 7.2. Case 2. p = q, ξ0 = η0 ............................... 106 7.3. Case 3. p < q ........................................ 107 Chapter 8. The Eigenvalues for n Odd .......................... 119 8.1. Case 1. p = q ........................................ 119 8.2. Case 2. p < q ........................................ 123 8.3. Case 3. p > q ........................................ 131 Chapter 9. Completeness of the Generalized Eigenf unctions .... 139 9.1. Completeness for n Even ............................... 139 9.2. Completeness for n Odd ................................ 142 Chapter 10.The Case L = T, Degenerate Irregular Examples ...... 147 10.1.The Case L = T ........................................ 147 10.2.Two Degenerate Irregular Examples ..................... 150 10.3.The Case n = 4, L = T ................................. 153 Chapter 11.Unsolved Problems .................................. 165 Chapter 12.Appendix ........................................... 169 Bibliography .................................................. 171 Index ......................................................... 175