Title page......Page 1
Contents......Page 3
Introduction......Page 6
1.1. Lifting and open mapping theorems......Page 10
1.2. Some classes of linear operators......Page 14
1.4. Fredholm operators that depend continuously on a parameter......Page 37
1.5. Some information from complex analysis......Page 41
A. Interpolation of entire functions of finite order......Page 43
B. Some information from the complex analysis in several variables......Page 63
C. Some problems of infinite-dimensional complex analysis......Page 69
1.6. Fredholm operators that depend holomorphically on a parameter......Page 75
1.7. Image and cokernel of a Fredholm morphism in spaces of holomorphic sections......Page 83
1.8. Image and cokernel of a Fredholm morphism in spaces of holomorphic sections with bounds......Page 85
1.9. Comments and references......Page 95
2.1. Basic spaces and operators......Page 99
2.2. Fourier transform on the group of periods......Page 101
2.3. Comments and references......Page 110
3.1. Floquet-Bloch solutions. Quasimomentums and Floquet exponents......Page 111
3.2. Floquet expansion of solutions of exponential growth......Page 118
3.3. Completeness of Floquet solutions in a class of solutions of faster growth......Page 120
A. Elliptic systems......Page 123
B. Hypoelliptic equations and systems......Page 124
C. Pseudodifferential equations......Page 125
D. Smoothness of coefficients......Page 126
3.5. Comments and references......Page 129
4.1. Distribution of quasimomentums and decreasing solutions......Page 132
4.2. Solvability of non-homogeneous equations......Page 154
4.3. Bloch property......Page 157
4.4. Quasimomentum dispersion relation. Bloch variety......Page 158
4.5. Some problems of spectral theory......Page 165
4.6. Positive solutions......Page 179
4.7 Comments and references......Page 190
5.1. Abstract hypoelliptic evolution equations on the whole axis......Page 194
5.2. Some degenerate cases......Page 216
5.3. Cauchy problem for abstract parabolic equations......Page 231
A. Elliptic problems......Page 251
B. Parabolic problems......Page 262
5.5. Comments and references......Page 266
6.1. Equations with deviating arguments......Page 270
6.2. Equations with coefficients that do not depend on some arguments......Page 275
6.3. Invariant differential equations on Riemannian symmetric spaces of non-compact type......Page 290
6.4. Comments and references......Page 304
Bibliography......Page 310
Index of symbols......Page 351
Index......Page 355