Fourier Analysis

01.0_pp_i_iv_Frontmatter
02.0_pp_v_vi_Epigraph
03.0_pp_vii_x_Contents
04.0_pp_xi_xii_Foreword
05.0_pp_xiii_xiv_Preface
06.0_pp_1_2_Fourier_Series
06.1_pp_3_5_Introduction
06.2_pp_6_10_Proof_of_Fejers_theorem
06.3_pp_11_14_Weyls_equidistribution_theorem
06.4_pp_15_18_The_Weierstrass_polynomial_approximation_theorem
06.5_pp_19_20_A_second_proof_of_Weierstrasss_theorem
06.6_pp_21_23_Hausdorffs_moment_problem
06.7_pp_24_27_The_importance_of_linearity
06.8_pp_28_31_Compass_and_tides
06.9_pp_32_34_The_simplest_convergence_theorem
06.10_pp_35_37_The_rate_of_convergence
06.11_pp_38_41_A_nowhere_differentiable_function
06.12_pp_42_45_Reactions
06.13_pp_46_49_Monte_Carlo_methods
06.14_pp_50_55_Mathematical_Brownian_motion
06.15_pp_56_58_Pointwise_convergence
06.16_pp_59_61_Behaviour_at_points_of_discontinuity_I
06.17_pp_62_66_Behaviour_at_points_of_discontinuity_II
06.18_pp_67_73_A_Fourier_series_divergent_at_a_point
06.19_pp_74_76_Pointwise_convergence_the_answer
07.0_pp_77_78_Some_Differential_Equations
07.1_pp_79_82_The_undisturbed_damped_oscillator_does_not_explode
07.2_pp_83_87_The_disturbed_damped_linear_oscillator_does_not_explode
07.3_pp_88_92_Transients
07.4_pp_93_98_The_linear_damped_oscillator_with_periodic_input
07.5_pp_99_103_A_non-linear_oscillator_I
07.6_pp_104_112_A_non-linear_oscillator_II
07.7_pp_113_115_A_non-linear_oscillator_III
07.8_pp_116_120_Poisson_summation
07.9_pp_121_123_Dirichlets_problem_for_the_disc
07.10_pp_124_130_Potential_theory_with_smoothness_assumptions
07.11_pp_131_133_An_example_of_Hadamard
07.12_pp_134_142_Potential_theory_without_smoothness_assumptions
08.0_pp_143_144_Orthogonal_Series
08.1_pp_145_149_Mean_square_approximation_I
08.2_pp_150_154_Mean_square_approximation_II
08.3_pp_155_158_Mean_square_convergence
08.4_pp_159_165_The_isoperimetric_problem_I
08.5_pp_166_169_The_isoperimetric_problem_II
08.6_pp_170_174_The_SturmLiouville_equation_I
08.7_pp_175_178_Liouville
08.8_pp_179_184_The_SturmLiouville_equation_II
08.9_pp_185_190_Orthogonal_polynomials
08.10_pp_191_196_Gaussian_quadrature
08.11_pp_197_200_Linkages
08.12_pp_201_206_Tchebychev_and_uniform_approximation_I
08.13_pp_207_211_The_existence_of_the_best_approximation
08.14_pp_212_218_Tchebychev_and_uniform_approximation_II
09.0_pp_219_220_Fourier_Transforms
09.1_pp_221_225_Introduction
09.2_pp_226_229_Change_in_the_order_of_integration_I
09.3_pp_230_239_Change_in_the_order_of_integration_II
09.4_pp_240_244_Fejers_theorem_for_Fourier_transforms
09.5_pp_245_252_Sums_of_independent_random_variables
09.6_pp_253_258_Convolution
09.7_pp_259_264_Convolution_on_T
09.8_pp_265_269_Differentiation_under_the_integral
09.9_pp_270_273_Lord_Kelvin
09.10_pp_274_281_The_heat_equation
09.11_pp_282_284_The_age_of_the_earth_I
09.12_pp_285_288_The_age_of_the_earth_II
09.13_pp_289_291_The_age_of_the_earth_III
09.14_pp_292_294_Weierstrasss_proof_of_Weierstrasss_theorem
09.15_pp_295_299_The_inversion_formula
09.16_pp_300_307_Simple_discontinuities
09.17_pp_308_314_Heat_flow_in_a_semi-infinite_rod
09.18_pp_315_323_A_second_approach
09.19_pp_324_331_The_wave_equation
09.20_pp_332_334_The_transatlantic_cable_I
09.21_pp_335_337_The_transatlantic_cable_II
09.22_pp_338_343_Uniqueness_for_the_heat_equation_I
09.23_pp_344_346_Uniqueness_for_the_heat_equation_II
09.24_pp_347_348_The_law_of_errors
09.25_pp_349_356_The_central_limit_theorem_I
09.26_pp_357_362_The_central_limit_theorem_II
10.0_pp_363_364_Further_Developments
10.1_pp_365_367_Stability_and_control
10.2_pp_368_371_Instability
10.3_pp_372_378_The_Laplace_transform
10.4_pp_379_385_Deeper_properties
10.5_pp_386_394_Poles_and_stability
10.6_pp_395_402_A_simple_time_delay_equation
10.7_pp_403_406_An_exception_to_a_rule
10.8_pp_407_412_Many_dimensions
10.9_pp_413_417_Sums_of_random_vectors
10.10_pp_418_424_A_chi_squared_test
10.11_pp_425_428_Haldane_on_fraud
10.12_pp_429_433_An_example_of_outstanding_statistical_treatment_I
10.13_pp_434_435_An_example_of_outstanding_statistical_treatment_II
10.14_pp_436_442_An_example_of_outstanding_statistical_treatment_III
10.15_pp_443_450_Will_a_random_walk_return
10.16_pp_451_454_Will_a_Brownian_motion_return
10.17_pp_455_460_Analytic_maps_of_Brownian_motion
10.18_pp_461_466_Will_a_Brownian_motion_tangle
10.19_pp_467_470_La_Famille_Picard_va_a_Monte_Carlo
11.0_pp_471_472_Other_Directions
11.1_pp_473_474_The_future_of_mathematics_viewed_from_1800
11.2_pp_475_477_Who_was_Fourier_I
11.3_pp_478_480_Who_was_Fourier_II
11.4_pp_481_483_Why_do_we_compute
11.5_pp_484_487_The_diameter_of_stars
11.6_pp_488_490_What_do_we_compute
11.7_pp_491_496_Fourier_analysis_on_the_roots_of_unity
11.8_pp_497_499_How_do_we_compute
11.9_pp_500_502_How_fast_can_we_multiply
11.10_pp_503_505_What_makes_a_good_code
11.11_pp_506_508_A_little_group_theory
11.12_pp_509_512_A_good_code
11.13_pp_513_518_A_little_more_group_theory
11.14_pp_519_524_Fourier_analysis_on_finite_Abelian_groups
11.15_pp_525_531_A_formula_of_Euler
11.16_pp_532_538_An_idea_of_Dirichlet
11.17_pp_539_545_Primes_in_some_arithmetical_progressions
11.18_pp_546_551_Extension_from_real_to_complex_variable
11.19_pp_552_557_Primes_in_general_arithmetical_progressions
11.20_pp_558_559_A_word_from_our_founder
12.0_pp_560_562_The_circle_T
13.0_pp_563_564_Continuous_function_on_closed_bounded_sets
14.0_pp_565_574_Weakening_hypotheses
15.0_pp_575_576_Ode_to_a_galvanometer
16.0_pp_577_579_The_principle_of_the_argument
17.0_pp_580_580_Chase_the_constant
18.0_pp_581_584_Are_share_prices_in_Brownian_motion
19.0_pp_585_592_Index