Representation Theorems in Hardy Spaces (London Mathematical Society Student Texts, Series Number 74)

The Theory Of Hardy Spaces Has Close Connections To Many Branches Of Mathematics Including Fourier Analysis, Harmonic Analysis, Singular Integrals, Potential Theory And Operator Theory, And Has Found Essential Applications In Robust Control Engineering. For Each Application, The Ability To Represent Elements Of These Classes By Series Or Integral Formulas Is Of Utmost Importance. This Self-contained Text Provides An Introduction To A Wide Range Of Representation Theorems And Provides A Complete Description Of The Representation Theorems With Direct Proofs For Both Classes Of Hardy Spaces: Hardy Spaces Of The Open Unit Disc And Hardy Spaces Of The Upper Half Plane. With Over 300 Exercises, Many With Accompanying Hints, This Book Is Ideal For Those Studying Advanced Complex Analysis, Function Theory Or Theory Of Hardy Spaces. Advanced Undergraduate And Graduate Students Will Find The Book Easy To Follow, With A Logical Progression From Basic Theory To Advanced Research. Fourier Series -- Abel-poisson Means -- Harmonic Functions In The Unit Disc -- Logarithmic Convexity -- Analytic Functions In The Unit Disc -- Norm Inequalities For The Conjugate Function -- Blaschke Products And Their Applications -- Interpolating Linear Operators -- The Fourier Transform -- Poisson Integrals -- Harmonic Functions In The Upper Half Plane -- The Plancherel Transform -- Analytic Functions In The Upper Half Plane -- The Hilbert Transform On R -- Topics From Real Analysis -- A Panoramic View Of The Representation Theorems. Javad Mashreghi. Includes Bibliographical References (p. 367-368) And Index. 00. 9780521732017 01.0_pp_i_vi_Frontmatter 02.0_pp_vii_x_Contents 03.0_pp_xi_xii_Preface 04.0_pp_1_20_Fourier_series 05.0_pp_21_54_AbelPoisson_means 06.0_pp_55_80_Harmonic_functions_in_the_unit_disc 07.0_pp_81_102_Logarithmic_convexity 08.0_pp_103_130_Analytic_functions_in_the_unit_disc 09.0_pp_131_154_Norm_inequalities_for_the_conjugate_function 10.0_pp_155_186_Blaschke_products_and_their_applications 11.0_pp_187_206_Interpolating_linear_operators 12.0_pp_207_224_The_Fourier_transform 13.0_pp_225_246_Poisson_integrals 14.0_pp_247_262_Harmonic_functions_in_the_upper_half_plane 15.0_pp_263_278_The_Plancherel_transform 16.0_pp_279_300_Analytic_functions_in_the_upper_half_plane 17.0_pp_301_338_The_Hilbert_transform_on 18.0_pp_339_350_Topics_from_real_analysis 19.0_pp_351_366_A_panoramic_view_of_the_representation_theorems 20.0_pp_367_368_Bibliography 21.0_pp_369_372_Index