Table of contents

Contents Introduction § 1. Operator spaces and function spaces § 2. Estimates of singular numbers based on the method of piecewise-polynomial approximation § 3. Interpolation methods § 4. General results on estimates (statements) § 5. Proof of the main results on estimates § 6. Operators with a difference kernel § 7. Tests for nuclearity § 8. Multipliers in classes of kernels of integral operators § 9. Analytical results for the multiplier problem § 10. Operators with a homogeneous difference kernel § 11. Some special cases Appendix. M. Z. Solomyak, The Interpolation of bilinear maps from function spaces into operator spaces References

Contents § 6. The representations and § 7. The perfectness of the lattices and . Characteristic functions § 8. The algebras and the representations § 9. Complete irreducibility of the representations and References

Contents Chapter III. A study, based on the mean-value formula, of spectral decompositions for second-order elliptic operators § 1. Basic notation and definitions § 2. Properties of fundamental functions § 3. An estimate of the remainder term of the spectral function in the L₂ metric and its consequences § 4. A uniform estimate of the remainder term of the spectral function § 5. The general case of second-order elliptic operators References