| Preface |
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v | (8) |
| Notation |
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xiii | |
| Prologue: Sequences |
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1 | (24) |
| 1 Countability |
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1 | (6) |
| 2 Separability |
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7 | (5) |
| 3 The Diagonal Procedure |
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12 | (6) |
| 4 Bounded Sequences of Continuous Linear Maps |
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18 | (7) |
| I FUNCTION SPACES AND THEIR DUALS |
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25 | (160) |
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1 The Space of Continuous Functions on a Compact Set |
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27 | (22) |
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28 | (3) |
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2 The Stone-Weierstrass Theorems |
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31 | (11) |
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42 | (7) |
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2 Locally Compact Spaces and Radon Measures |
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49 | (48) |
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49 | (8) |
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57 | (11) |
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3 Positive Radon Measures |
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68 | (18) |
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3A Positive Radon Measures on R and the Stieltjes Integral |
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71 | (3) |
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3B Surface Measure on Spheres in R^(d) |
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74 | (12) |
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4 Real and Complex Radon Measures |
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86 | (11) |
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97 | (46) |
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1 Definitions, Elementary Properties, Examples |
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97 | (8) |
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105 | (6) |
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3 The Riesz Representation Theorem |
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111 | (12) |
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3A Continuous Linear Operators on a Hilbert Space |
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112 | (2) |
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3B Weak Convergence in a Hilbert Space |
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114 | (9) |
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123 | (20) |
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143 | (42) |
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1 Definitions and General Properties |
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143 | (16) |
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159 | (10) |
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169 | (16) |
| II OPERATORS |
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185 | (70) |
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187 | (26) |
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1 Operators on Banach Spaces |
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187 | (14) |
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2 Operators in Hilbert Spaces |
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201 | (12) |
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2A Spectral Properties of Hermitian Operators |
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203 | (2) |
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2B Operational Calculus on Hermitian Operators |
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205 | (8) |
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213 | (42) |
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213 | (21) |
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1A Spectral Properties of Compact Operators |
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217 | (17) |
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2 Compact Selfadjoint Operators |
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234 | (21) |
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2A Operational Calculus and the Fredholm Equation |
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238 | (2) |
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240 | (15) |
| III DISTRIBUTIONS |
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255 | (124) |
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7 Definitions and Examples |
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257 | (30) |
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257 | (10) |
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257 | (2) |
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1B Convergence in Function Spaces |
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259 | (2) |
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261 | (1) |
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1D C^(Infinity) Partitions of Unity |
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262 | (5) |
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267 | (13) |
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267 | (1) |
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268 | (3) |
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2C Restriction and Extension of a Distribution to an Open Set |
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271 | (1) |
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2D Convergence of Sequences of Distributions |
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272 | (1) |
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272 | (1) |
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273 | (7) |
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280 | (7) |
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3A Distributions of Finite Order |
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280 | (1) |
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3B The Support of a Distribution |
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281 | (1) |
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3C Distributions with Compact Support |
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281 | (6) |
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8 Multiplication and Differentiation |
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287 | (30) |
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287 | (5) |
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292 | (14) |
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3 Fundamental Solutions of a Differential Operator |
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306 | (11) |
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307 | (3) |
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310 | (1) |
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3C The Cauchy-Riemann Operator |
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311 | (6) |
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9 Convolution of Distributions |
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317 | (32) |
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1 Tensor Product of Distributions |
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317 | (7) |
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2 Convolution of Distributions |
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324 | (13) |
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324 | (1) |
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325 | (7) |
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2C Convolution of a Distribution with a Function |
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332 | (5) |
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337 | (12) |
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3A Primitives and Sobolev's Theorem |
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337 | (3) |
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340 | (3) |
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3C Fundamental Solutions and Partial Differential Equations |
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343 | (3) |
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343 | (6) |
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10 The Laplacian on an Open Set |
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349 | (30) |
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1 The spaces H^(1)(Omega) and H^(1)(0)(Omega) |
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349 | (14) |
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363 | (16) |
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366 | (1) |
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367 | (1) |
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368 | (1) |
| Answers to the Exercises |
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379 | (8) |
| Index |
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387 | |
