دانلود کتاب Functional Operators (AM-22), Volume 2: The Geometry of Orthogonal Spaces. (AM-22)

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TABLE OF CONTENTS\nPreface\nCHAPTER I. FOURIER TRANSFORMS IN L1 (One Variable)\n §1. Elementary properties\n §2. Riemann Lebesgue Lemma\n §3. Convolution of two functions\n §4. Derivative of a function and its transform\n §5. Inversion formula\n §6. Uniqueness of Fourier transform\n §7. Summability theorems\n §8. Some applications of summability-theorems\n §9. Continuity in norm\n §10. Summability in norm\n §11. Derivatives of a function and their transforms\n §12. Degree of approximation\n §13. Abel’s theorem\n §14. Abel and Gauss summability\n §15. Boundary values\n §16. Mean values\n §17. Tauberian theorems\nCHAPTER II. FOURIER TRANSFORMS IN L1 (Several Variables)\n §1. Riemann Lebesgue Lemma; Composition:, Convolution\n §2. Uniqueness theorem\n §3. Gauss summability formula\n §4. Gauss summability theorem\n §5. Application of summability-theorem\n §6. Norms, Continuity, Parseval relations\n §7. Radial functions\n §8. General summability for radial functions\nCHAPTER III. Lp-SPACES\n §1. Metric spaces\n §2. Completion of a metric space\n §3. Banach spaces\n §4. Linear operations\n §5. Lp spaces\n §6. Continuity, summability and approximation in Lp norm\nCHAPTER IV. FOURIER TRANSFORM IN L2\n §1. Transformations in Hilbert space\n §2. Plancherel\'s theorem\n §3. General summability\n §4. Several variables\n §5. Radial functions\n §6. Derivatives and their transforms\n §7. Boundary values\n §8. Simple type of bounded transformation\n §9. Bounded transformations commutative with translations\n §10. Closure of translations\nCHAPTER V. GENERAL TRANSFORMS IN L2\n §1. General unitary transformations in L2 (0,∞)\n §2. Watson transforms\n §3. Functional equation associated with Watson transform\nCHAPTER VI. GENERAL TAUBERIAN THEOREMS\n §1. Introduction\n §2. Preliminary lemmas\n §3. Tauberian theorems; Averages on (-∞,∞)\n §4. Averages on (0,∞)\n §5. Special cases\nNOTES