Author | Kuchment, Peter. author |
---|---|
Title | Floquet Theory for Partial Differential Equations [electronic resource] / by Peter Kuchment |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8573-7 |
Descript | XIV, 354 p. online resource |
1. Holomorphic Fredholm Operator Functions -- 1.1. Lifting and open mapping theorems -- 1.2. Some classes of linear operators -- 1.3. Banach vector bundles -- 1.4. Fredholm operators that depend continuously on a parameter -- 1.5. Some information from complex analysis -- 1.6. Fredholm operators that depend holomorphically on a parameter -- 1.7. Image and cokernel of a Fredholm morphism in spaces of holomorphic sections -- 1.8. Image and cokernel of a Fredholm morphism in spaces of holomorphic sections with bounds -- 1.9. Comments and references -- 2. Spaces, Operators and Transforms -- 2.1. Basic spaces and operators -- 2.2. Fourier transform on the group of periods -- 2.3. Comments and references -- 3. Floquet Theory for Hypoelliptic Equations and Systems in the Whole Space -- 3.1. Floquet โ Bloch solutions. Quasimomentums and Floquet exponents -- 3.2. Floquet expansion of solutions of exponential growth -- 3.3. Completeness of Floquet solutions in a class of solutions of faster growth -- 3.4. Other classes of equations -- 3.5. Comments and references -- 4. Properties of Solutions of Periodic Equations -- 4.1. Distribution of quasimomentums and decreasing solutions -- 4.2. Solvability of non-homogeneous equations -- 4.3. Bloch property -- 4.4. Quasimomentum dispersion relation. Bloch variety -- 4.5. Some problems of spectral theory -- 4.6. Positive solutions -- 4.7. Comments and references -- 5. Evolution Equations -- 5.1. Abstract hypoelliptic evolution equations on the whole axis -- 5.2. Some degenerate cases -- 5.3. Cauchy problem for abstract parabolic equations -- 5.4. Elliptic and parabolic boundary value problems in a cylinder -- 5.5. Comments and references -- 6. Other Classes of Problems -- 6.1. Equations with deviating arguments -- 6.2. Equations with coefficients that do not depend on some arguments -- 6.3. Invariant differential equations on Riemannian symmetric spaces of non-compact type -- 6.4. Comments and references -- Index of symbols