Applied Hyperfunction Theory

Series Editor's Preface. Preface. 1. Introduction. 2. Operations on Hyperfunctions. 3. Basic Hyperfunctions. 4. Hyperfunctions Depending on Parameters. 5. Fourier Transformation. 6. Fourier Transformation of Power-Type Hyperfunctions. 7. Upper (Lower)-Type Hyperfunctions. 8. Fourier Transforms - Existence and Regularity. 9. Fourier Transformation - Asymptotic Behaviour. 10. Periodic Hyperfunctions and Fourier Series. 11. Analytic Continuation and Projection of Hyperfunctions. 12. Products of Hyperfunctions. 13. Convolution of Hyperfunctions. 14. Convolution of Periodic Hyperfunctions. 15. Hilbert Transformation, Conjugate Hyperfunction. 16. Poisson-Schwarz Integration Formulae. 17. Integral Equations. 18. Laplace Transformation. Epilogue. References. Appendices A: Symbols. B: Functions, Hyperfunctions and Generating Functions. C: Special Functions. D: Power-Type Hyperfunctions with Negative Integer Power. E: Upper-Type and Lower-Type Hyperfunctions. F: Hyperfunctions and Generating Functions. G: Convolutions. H: Hilbert Transforms. I: Fourier Transforms. J: Laplace Transforms. K: Cosine Transforms and Sine Transforms. Index.