Functional AnalysisCourier Corporation, 1 janv. 2000 - 532 pages Excellent treatment of the subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed and metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach theorem and its consequences, spectral notions, square roots, a spectral decomposition theorem, and many other related subjects. Chapters conclude with exercises intended to test and reinforce reader’s understanding of text material. A glossary of definitions, detailed proofs of theorems, bibliography, and index of symbols round out this comprehensive text. 1966 edition. |
Table des matières
III | 3 |
IV | 7 |
V | 15 |
VI | 18 |
VII | 19 |
VIII | 20 |
X | 21 |
XI | 25 |
CXXI | 253 |
CXXII | 257 |
CXXIII | 258 |
CXXIV | 259 |
CXXV | 260 |
CXXVI | 261 |
CXXVII | 271 |
CXXVIII | 273 |
XII | 33 |
XIII | 36 |
XIV | 37 |
XV | 38 |
XVII | 39 |
XVIII | 40 |
XIX | 43 |
XX | 45 |
XXI | 48 |
XXII | 49 |
XXIII | 50 |
XXV | 51 |
XXVI | 52 |
XXVII | 58 |
XXVIII | 59 |
XXIX | 60 |
XXXI | 61 |
XXXII | 64 |
XXXIII | 67 |
XXXIV | 72 |
XXXV | 73 |
XXXVI | 74 |
XXXVIII | 75 |
XXXIX | 76 |
XL | 80 |
XLI | 82 |
XLII | 84 |
XLIV | 85 |
XLVI | 86 |
XLVII | 90 |
XLVIII | 93 |
XLIX | 96 |
L | 98 |
LI | 103 |
LII | 107 |
LIII | 108 |
LIV | 109 |
LV | 112 |
LVI | 118 |
LVII | 121 |
LVIII | 122 |
LIX | 126 |
LX | 129 |
LXI | 131 |
LXII | 133 |
LXIII | 135 |
LXIV | 136 |
LXVI | 138 |
LXVII | 140 |
LXIX | 141 |
LXX | 143 |
LXXI | 144 |
LXXII | 146 |
LXXIII | 149 |
LXXIV | 153 |
LXXV | 155 |
LXXVI | 157 |
LXXVII | 160 |
LXXVIII | 161 |
LXXIX | 162 |
LXXXII | 163 |
LXXXIII | 166 |
LXXXIV | 167 |
LXXXV | 168 |
LXXXVI | 172 |
LXXXVII | 174 |
LXXXVIII | 175 |
XCI | 176 |
XCII | 182 |
XCIII | 184 |
XCIV | 187 |
XCV | 188 |
XCVI | 195 |
XCVII | 196 |
C | 197 |
CI | 203 |
CII | 205 |
CIII | 209 |
CIV | 211 |
CV | 214 |
CVI | 215 |
CVII | 216 |
CX | 218 |
CXI | 227 |
CXII | 229 |
CXIII | 230 |
CXIV | 231 |
CXV | 238 |
CXVI | 243 |
CXVII | 244 |
CXVIII | 245 |
CXIX | 246 |
CXX | 250 |
CXXIX | 274 |
CXXX | 275 |
CXXXI | 276 |
CXXXII | 277 |
CXXXIII | 279 |
CXXXIV | 281 |
CXXXV | 283 |
CXXXVI | 286 |
CXXXVII | 289 |
CXXXVIII | 294 |
CXXXIX | 295 |
CXL | 296 |
CXLIII | 297 |
CXLIV | 300 |
CXLV | 304 |
CXLVII | 306 |
CXLVIII | 307 |
CLI | 308 |
CLII | 311 |
CLIII | 315 |
CLIV | 319 |
CLV | 322 |
CLVII | 327 |
CLVIII | 336 |
CLIX | 342 |
CLX | 348 |
CLXI | 350 |
CLXII | 351 |
CLXV | 352 |
CLXVI | 355 |
CLXVII | 362 |
CLXVIII | 367 |
CLXIX | 373 |
CLXX | 374 |
CLXXI | 375 |
CLXXII | 376 |
CLXXIII | 379 |
CLXXIV | 383 |
CLXXV | 386 |
CLXXVI | 389 |
CLXXVII | 390 |
CLXXVIII | 391 |
CLXXIX | 393 |
CLXXX | 405 |
CLXXXI | 406 |
CLXXXII | 407 |
CLXXXIII | 409 |
CLXXXIV | 411 |
CLXXXV | 412 |
CLXXXVI | 415 |
CLXXXVII | 417 |
CLXXXVIII | 418 |
CLXXXIX | 419 |
CXC | 420 |
CXCI | 426 |
CXCII | 430 |
CXCIII | 431 |
CXCIV | 432 |
CXCV | 433 |
CXCVI | 438 |
CXCVIII | 442 |
CXCIX | 443 |
CC | 444 |
CCI | 445 |
CCII | 448 |
CCIII | 450 |
CCIV | 458 |
CCV | 459 |
CCVI | 460 |
CCVII | 461 |
CCVIII | 469 |
CCIX | 470 |
CCX | 471 |
CCXI | 472 |
CCXII | 478 |
CCXIII | 483 |
CCXV | 484 |
CCXVI | 485 |
CCXVII | 488 |
CCXVIII | 493 |
CCXX | 494 |
CCXXI | 495 |
CCXXII | 498 |
CCXXIII | 516 |
CCXXIV | 520 |
CCXXV | 521 |
CCXXVI | 522 |
CCXXVII | 523 |
524 | |
526 | |
CCXXX | 530 |
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Expressions et termes fréquents
adjoint arbitrary assume Banach algebra Banach space basis bounded linear functional bounded linear transformation Cauchy sequence chapter clearly closed subspace commutes complete orthonormal set completely continuous completes the proof complex numbers conjugate space consider continuous functions convergent subsequence convex D₁ defined definition denote dense E₁ E₂ eigenvalues elements example Exercise exists finite follows functional ƒ Hence Hilbert space identity implies inequality inner product space integral inverse isometry lemma limit point linear transformation linearly independent M₁ M₂ mapping metric space nonzero normal transformation normed linear space notation notion open set orthogonal projection Po(A polynomials prove real numbers result satisfied scalar self-adjoint operators self-adjoint transformation sequence of points sesquilinear functional shown space and let spectral theorem spectrum subset Suppose topological space vector space verify x₁ y₁ zero