Applied Analysis Index

Applied Analysis Index - Index C-semigroup, 114, 163 L 1...

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Unformatted text preview: Index C-semigroup, 114, 163 L 1 norm, 4 L ∞ norm, 5 L p spaces, 351 local, 362-net, 24 σ-algebra, 335 Borel, 336, 338 σ-finite, 337 absolute convergence, 8 in a normed linear space, 33 action, 419 activator, 409 adjoint of a bounded operator, 193 of an unbounded operator, 246 advection-diffusion equation, 279 Airy’s equation, 330 algebra, 109 almost everywhere, 15, 340 almost periodic function, 135 analytic, 220 annihilation operator, 147 antilinear, 126 approximate identity, 151 approximate spectrum, 241 approximation scheme, 114 consistent, 114 convergent, 114 stable, 115 Arzel` a-Ascoli theorem, 45 asymptotically stable, 235, 404 averaging kernel, 260 backwards heat equation, 164 Baker-Campbell-Hausdorff formula, 123 ball closed, 14 open, 14 unit, 4 Banach algebra, 39 Banach space, 8, 91 of linear operators, 110 Banach-Alaoglu theorem, 120, 208 Banach-Steinhaus theorem, 204 base of open sets, 84 basis Hamel, 94 orthonormal, 133 Schauder, 94 Bernstein polynomials, 40 Bessel function, spherical, 279 Bessel’s inequality, 137 bifurcation equation, 425 bifurcation theory, 399 Biot-Savart law, 284 Birkhoff ergodic theorem, 204 Bolzano-Weierstrass theorem, 23 Borel σ-algebra, 336, 338 set, 336 Born approximation, 69 boundary, 88 boundary conditions, 250 boundary value problem, 69, 249 bounded from above, 9 from below, 9 function, 11 430 Index 431 linear operator, 95 set, 9 bounded linear transformation theorem, 100 brachistochrone problem, 413 Brownian motion, 327 calculus of variations, 410, 420 Cantor function, 32 Cantor set, 16 Cartesian product, 3 Cauchy sequence, 7 unordered sum, 136 Cauchy-Schwarz inequality, 128, 357 Central limit theorem, 320 chain rule, 388 characteristic function of a random variable, 323 of a set, 343 characteristic polynomial, 217 circle map, 172 classical solution, 370 closed ball, 14 operator, 247 set, 15 closure, 16, 88 sequential, 86 cluster point, 31 codimension, 187, 212 coercive, 34, 211 commutator, 109 compact metric space, 25 operator, 110 relatively, 27 support, 39 topological space, 83 compact resolvent, 227 complete measure space, 339 complete metric space, 8 of continuous functions, 38 complete orthonormal set, 139 completion of a measure space, 339 of a metric space, 19 complex measure, 337 conjugate exponent, Sobolev, 366 conjugate linear, 126 connected, 89 Continuity theorem, 325 continuous extension, 100 function, 12 in L p , 376 random variable, 320 spectrum, 219 topological space, 83 uniformly, 13, 27 contraction, 61 contraction mapping theorem, 62 convergence absolute, 8 in distribution of random variables, 324 of a sequence, 6 of series, 8 pointwise, 35 topological space, 82 unconditional, 136 uniform, 36 weak in Hilbert space, 204 convex function, 209 set, 4 convolution, 150, 298, 359 operator, 329 theorem, 154, 309 countable, 30 countably additive, 335 counting measure, 337 covariance matrix of a Gaussian, 331 cover, 24 creation operator, 147 critical point, 381, 410 cylinder set, 85 d’Alembert’s solution, 185...
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This note was uploaded on 03/23/2012 for the course AMATH 567 taught by Professor A.g during the Fall '11 term at University of Washington.

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Applied Analysis Index - Index C-semigroup, 114, 163 L 1...

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