Table of Contents

1. Introduction and overview 1

2. Preliminaries 26

3. Cones of n-ary m-ics and their duals 36

4. Representations as sums of m-th powers 51

5. Binary forms and ternary quartics 61

6. Moment problems 76

7. Quadrature problems 88

8. Representations of h 100

r n,m

9. Minimal representations of h 121

n,m

10. Further questions 137

11. Bibliography 148

v