Author | Zaanen, Adriaan C. author |
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Title | Continuity, Integration and Fourier Theory [electronic resource] / by Adriaan C. Zaanen |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1989 |
Connect to | http://dx.doi.org/10.1007/978-3-642-73885-2 |
Descript | VIII, 251 p. online resource |
1. The Space of Continuous Functions -- 1. Subsets of ?k -- 2. The Space of Continuous Functions -- 3. Lattice Properties of the Space of Real Continuous Functions -- 2. Theorems of Korovkin and Stone-Weierstrass -- 4. Theorems of Korovkin and Weierstrass -- 5. The Stone-Weierstrass Theorem -- 6. The Complex Stone-Weierstrass Theorem -- 3. Fourier Series of Continuous Functions -- 7. Trigonometric Polynomials -- 8. Fourier Series -- 9. Fejรฉrโs Theorem on Uniform Convergence of Cesaro Means -- 10. Fourier Coefficients and Orders of Magnitude -- 4. Integration and Differentation -- 11. Measure -- 12. Integral -- 13. Product Integral, Fubiniโs Theorem and Convolution -- 14. Differentiation of the Integral -- 15. Measurability, Continuity and Differentiability -- 5. Spaces Lp and Convolutions -- 16. Hรถlderโs Inequality -- 17. Spaces Lp -- 18. Convolution -- 19. Convolution and Approximate Identities -- 6. Fourier Series of Summable Functions -- 20. Fourier Coefficients and the Fourier Transform -- 21. Pointwise Convergence of Cesaro Means and Abel Means -- 22. Pointwise Convergence of Fourier Series -- 23. Hilbert Space and the Space L2 -- 7. Fourier Integral -- 24. Some Useful Integrals -- 25. Inverse Fourier Transform -- 26. Convergence of the Inverse Fourier Transform -- 27. The Plancherel Theorem -- 8. Additional Results -- 28. The Wilbraham-Gibbs Phenomenon -- 29. Absolute Convergence -- 30. Positive Definite Functions -- 31. Equidistribution of Sequences -- 32. Functions of Analytic Type -- 33. The Hausdorff-Young Theorem -- 34. The Poisson Sum Formula -- 35. The Heat Equation -- 36. More on the Heat Equation -- 37. The Wave Equation -- References