Author | Schlichtkrull, Henrik. author |
---|---|
Title | Hyperfunctions and Harmonic Analysis on Symmetric Spaces [electronic resource] / by Henrik Schlichtkrull |
Imprint | Boston, MA : Birkhรคuser Boston, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5298-6 |
Descript | XIV, 186 p. online resource |
1. Hyperfunctions and Microlocal Analysis โ An Introduction -- 1.1. Hyperfunctions of one variable -- 1.2. Sheaves -- 1.3. Cohomology of sheaves -- 1.4. Hyperfunctions of several variables -- 1.5. The singular spectrum and microfunctions -- 1.6. Micro-differential operators -- 1.7. Notes -- 2. Differential Equations with Regular Singularities -- 2.1. Regular singularities for ordinary equations -- 2.2. Regular singularities for partial differential equations -- 2.3. Boundary values for a single equation -- 2.4. Example -- 2.5. Boundary values for a system of equations -- 2.6. Notes -- 3. Riemannian Symmetric Spaces and Invariant Differential Operators โ Preliminaries -- 3.1. Decomposition and integral formulas for semisimple Lie groups -- 3.2. Parabolic subgroups -- 3.3. Invariant differential operators -- 3.4. Notes -- 4. A Compact Imbedding -- 4.1. Construction and analytic structure of X? -- 4.2. Invariant differential operators on X? -- 4.3. Regular singularities -- 4.4. Notes -- 5. Boundary Values and Poisson Integral Representations -- 5.1. Poisson transformations -- 5.2. Boundary value maps -- 5.3. Spherical functions and their asymptotics -- 5.4. Integral representations -- 5.5. Notes and further results -- 6. Boundary Values on the Full Boundary -- 6.1. Partial Poisson transformations -- 6.2. Partial spherical functions and Poisson kernels -- 6.3. Boundary values and asymptotics -- 6.4. The bijectivity of the partial Poisson transformations -- 6.5. Notes and further results -- 7. Semisimple Symmetric Spaces -- 7.1. The orbits of symmetric subgroups -- 7.2. Root systems -- 7.3. A fundamental family of functions -- 7.4. A differential property -- 7.5. Asymptotic expansions -- 7.6. The case of equal rank -- 7.7. Examples -- 7.8. Notes and further results -- 8. Construction ff Functions with Integrable Square -- 8.1. The invariant measure on G/H -- 8.2. An important duality -- 8.3. Discrete series -- 8.4. Examples -- 8.5. Notes and further results