Table of contents

CONTENTS Introduction § 1. Siegel domains and affine-homogeneous cones § 2. Compound power functions and Siegel integrals § 3. Riemann-Liouville operators associated with homogeneous cones § 4. Hypergeometric functions on homogeneous cones § 5. Integral formulae in Siegel domains of the second kind § 6. V_δ-analytic functions in Siegel domains of the first kind References

CONTENTS Introduction § 1. Theorems on the convex hulls of the rearrangements of a vector (finite-dimensional case) § 2. The eigen- and singular values of the sum and product of matrices § 3. Two theorems on symmetric gauge functions § 4. Theorems on the convex hulls of the rearrangements of a vector (infinite-dimensional case) § 5. The eigen- and singular values of the sum and product of completely continuous operators References

CONTENTS Introduction § 1. Estimates for Faber polynomials within the domain § 2. Asymptotic formulae § 3. Convergence of Faber series within the domain § 4. Convergence of Faber series in the closed domain § 5. Series of Faber polynomials § 6. On the uniqueness of series of Faber polynomials § 7. Application of Faber polynomials to the interpolation of analytic functions § 8. Asymptotic behaviour of Faber polynomials with singular weight function § 9. Faber polynomials for an interval § 10. Further remarks and unsolved problems References