Lectures on Fourier Integrals. (AM-42), Volume 42

CONTENTS\nCHAPTER I: BASIC PROPERTIES OF TRIGONOMETRIC INTEGRALS\n	§1. Trigonometric Integrals Over Finite Intervals\n	§2. Trigonometric Integrals Over Infinite Intervals\n	§3. Order of Magnitude of Trigonometric, Integrals\n	§4. Uniform Convergence of Trigonometric Integrals\n	§5. The Cauchy Principal Value of Integrals\nCHAPTER II: REPRESENTATION — AND SUM FORMULAS\n	§6. A General Representation Formula\n	§7. The Dirichlet Integral and Related Integrals\n	§8. The Fourier Integral Formula\n	§9. The Wiener Formula\n	§10. The Poisson Summation Formula\nCHPATER III: THE FOURIER INTEGRAL THEOREM\n	§11. The Fourier Integral Theorem and the Inversion Formulas\n	§12. Trigonometric Integrals with e^-x\n	§13. The Absolutely Integrable Functions. Their Faltung and Their Summation\n	§14. Trigonometric Integrals with Rational Functions\n	§15. Trigonometric Integrals with e^-x\n	§16. Bessel Functions\n	§17. Evaluation of Certain Repeated Integrals\nCHAPTER IV: STIELTJES INTEGRALS\n	§18. The Function Class B\n	§19. Sequences of Functions of B\n	§20. Positive-Definite Functions\n	§21. Spectral Decomposition of Positive-Definite Functions An Application to Almost Periodic Functions\nCHAPTER V: OPERATIONS WITH FUNCTIONS OF THE CLASS JO\n	§22. The Question\n	§23. Multipliers\n	§24. Differentiation and Integration\n	§25. The Difference-Differential Equation\n	§26. The Integral Equation\n	§27. Systems of Equations\nCHAPTER VI: GENERALIZED TRIGONOMETRIC INTEGRALS\n	§28. Definition of the Generalized Trigonometric Integrals\n	§29. Further Particulars About the Functions of Jk\n	§30. Further Particulars About the Functions of Ik\n	§31. Convergence Theorems\n	§32. Multipliers\n	§33. Operator Equations\n	§34. Functional Equations\nCHAPTER VII: ANALYTIC AND HARMONIC FUNCTIONS\n	§35. Laplace Integrals\n	§36. Union of Laplace Integrals\n	§37. Representation of Given Functions by Laplace Integrals\n	§38. Continuation. Harmonic Functions\n	§39. Boundary Value Problems for Harmonic Functions\nCHAPTER VIII: QUADRATIC INTEGRABILITY\n	§40. The Parseval Equation\n	§41. The Theorem of Plancherel\n	§42. Hankel Transform\nCHAPTER IX: FUNCTIONS OF SEVERAL VARIABLES\n	§43. Trigonometric Integrals in Several Variables\n	§44. The Fourier Integral Theorem\n	§45. The Dirichlet Integral\n	§46. The Poisson Summation Formula\nAPPENDIX\n	Concerning Functions of Real Variables\n	Measurability\n	Summability\n	Differentiability\n	Approximation in the Mean\n	Complex Valued Functions\n	Extension of Functions\n	Summation of Repeated Integrals\nREMARKS - QUOTATIONS\nMONOTONIC FUNCTIONS, STIELTJES INTEGRALS AND HARMONIC ANALYSIS\n	Introduction\n	I: MONOTONIC FUNCTIONS\n		§1. Definition of the Monotonic Functions\n		§2. Continuity Intervals\n		§3. Sequences of Monotonic Functions\n	II: STIELTJES INTEGRALS\n		§4. Definition and Important Properties\n		§5. Uniqueness and Limit Theorems\n	III: HARMONIC ANALYSIS\n		§6. Fourier-Stieltjes Integrals\n		§7. Uniqueness and Limit Theorems\n		§8. Positive-Definite Functions\n		§9. Spectral Decomposition of Square Integrable Functions\nSYMBOLS - INDEX