Lecture Notes for 18.155, Fall 2004

Abstract

Introduction 1 1. Continuous functions 2 2. Measures and σ­algebras 10 3. Measureability of functions 16 4. Integration 19 5. Hilbert space 30 6. Test functions 34 7. Tempered distributions 42 8. Convolution and density 47 9. Fourier inversion 58 10. Sobolev embedding 63 11. Differential operators. 67 12. Cone support and wavefront set 83 13. Homogeneous distributions 96 14. Wave equation 97 15. Operators and kernels 98 16. Spectral theorem 99 17. Problems 103 18. Solutions to (some of) the problems 130 References 136

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