| Introduction Chapter 10. Existence and Approximation of Solutions of Differential Equations Summary 10.1. The Spaces Bp.k 10.2. Fundamental Solutions 10.3. The Equation P(D) u =f when 10.4. Comparison of Differential Operators 10.5. Approximation of Solutions of Homogeneous Differential Equations 10.6. The Equation P(D)u=f when f is in a Local Space 10.7. The Equation P(D) u =f when 10.8. The Geometrical Meaning of the Convexity Conditions Notes Chapter 11. Interior Regularity of Solutions of Differential Equations Summary 11.1. HypoeUiptic Operators 11.2. Partially Hypoelliptic Operators 11.3. Continuation of Differentiability 11.4. Estimates for Derivatives of High Order Notes Chapter 12. The Cauchy and Mixed Problems Summary 12.1 The Cauchy Problem for the Wave Equation 12.2 The Oscillatory Cauchy Problem for the Wave Equation 12.3 Necessary Conditions for Existence and Uniqueness of Solutions to the Cauchy Problem …… Chapter 13 Differential Operators of Constant Strength Chapter 14 Scattering Theory Chapter 15 Analytic Function Theory and Differential Equations Chapter 16 Convolution Equations Appendix A. Some Algebraic Lemmas Bibliography Index Index of Notation |
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