Gap and density theorems

N. Levinson9780821810262, 082181026X

Table of contents :
Title page……Page 1
Press……Page 2
Dedication……Page 3
Preface……Page 4
CONTENTS……Page 5
1. Introduction……Page 7
2. A closure theorem for $lambda_n>0$……Page 8
3. A closure theorem for $-infty < lambda_n < infty$……Page 11
4. A closure theorem involving Polya maximum density……Page 18
5. A related gap theorem……Page 20
6. An extension of the closure theorem……Page 22
7. Another type of theorem……Page 25
8. A theorem of Miss Cartwright……Page 26
9. The basic theorem……Page 31
10. A related function with real zeros……Page 35
11. Lemmas on the related function……Page 39
12. Proof of the basic theorem……Page 44
13. A related theorem……Page 48
14. Another related theorem……Page 50
15. Proof of an underlying inequality……Page 53
16. Proof of the main theorems……Page 61
17. Proof of a related inequality of Hardy and Levinson……Page 73
18. Introduction……Page 79
19. Proof of the basic theorem……Page 81
20. Related theorems……Page 87
21. The density theorem……Page 94
22. A function with zeros having a density……Page 98
23. Theorems of V. Bernstein……Page 106
24. A sharper set of theorems……Page 113
25. An extension of a theorem of Iyer……Page 128
26. Generalization of a problem of P61ya……Page 133
27. Proof of the inequality……Page 141
28. Proof of the theorem on functions of zero type……Page 151
29. Statement of the existence theorems……Page 159
30. Lemmas……Page 162
31. Proof of the main theorem……Page 177
32. Introduction……Page 192
33. Reduction to a lemma on biorthogonal functions……Page 197
34. Proof of the lemma……Page 201
35. Reduction of the general theorem to the basic lemma……Page 209
36. Existence of auxiliary functions……Page 213
37. Proof of the basic lemma……Page 219
38. Proofs of the remaining theorems……Page 224
39. A restricted higher indices theorem……Page 235
40. Proof of the theorem……Page 237
41. Theorems used……Page 249
AMS Colloquium Publications……Page 253