دانلود کتاب Complex proofs of real theorems

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The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics Chapter 1. Early triumphs -- 1.1. The Basel problem -- 1.2. The fundamental theorem of algebra -- Chapter 2. Approximation -- 2.1. Completeness of weighted powers -- 2.2. The Müntz approximation theorem -- Chapter 3. Operator theory -- 3.1. The Fuglede-Putnam theorem -- 3.2. Toeplitz operators -- 3.3. A theorem of Beurling -- 3.4. Prediction theory -- 3.5. The Riesz-Thorin convexity theorem -- 3.6. The Hilbert transform -- Chapter 4. Harmonic analysis -- 4.1. Fourier uniqueness via complex variables (d'après D.J. Newman) -- 4.2. A curious functional equation -- 4.3. Uniqueness and nonuniqueness for the Radon transform -- 4.4. The Paley-Wiener theorem -- 4.5. The Titchmarsh convolution theorem -- 4.6. Hardy's theorem -- Chapter 5. Banach algebras: the Gleason-Kahane-Żelazko theorem -- Chapter 6. Complex dynamics: the Fatou-Julia-Baker theorem -- Chapter 7. The prime number theorem -- Coda. Transonic airfoils and SLE -- Appendix A. Liouville's theorem in Banach spaces -- Appendix B. The Borel-Carathéodory inequality -- Appendix C. Phragmén-Lindelöf theorems -- Appendix D. Normal families