• Almost everywhere convergence for modified Bochner Riesz means at the critical index for [rho] [greater than or equal to] 2 

    Annoni, Marco, 1981- (University of Missouri--Columbia, 2010)
    The Fourier transform is a mathematical operation that can be used with its inverse to rewrite a function as a sum of waves. It has been a useful mathematical tool for many applied sciences. Sometimes Fourier inversion is ...
  • Conformal mappings and the Schwarz-Christoffel transformation 

    Heinen, Rebecca (University of Missouri--Columbia, 2017)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation ...
  • Counting theorems and inverse function theorems for analytic functions 

    Delibas, Hakan (University of Missouri--Columbia, 2017)
    In this master's thesis, we discuss the counting and Rouche's theorems. These theorems are used to find the roots of complex analytic functions.Also, we investigate the existence of the inverse function of an analytic ...
  • Directional time-frequency analysis with applications 

    Sansing, Christopher, 1979- (University of Missouri--Columbia, 2006)
    The purpose of this dissertation is to introduce a new directionally-sensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual time-frequency-direction ...
  • Distributional estimates for multilinear operators 

    Bilyk, Dmytro, 1979- (University of Missouri--Columbia, 2005)
    We prove that if a multilinear operator and all its adjoints map L1 x x L1 to L1/m,oo, then the distribution function of the operator applied to characteristic functions of sets of finite measure has exponential decay at ...
  • Harmonic functions and the Dirichlet problem 

    Mayfield, Caleb James (University of Missouri--Columbia, 2017)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and ...
  • Maximal Fourier integrals and multilinear multiplier operators 

    Nguyen, Hanh Van (Researcher on mathematics) (University of Missouri--Columbia, 2016)
    The first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the ...
  • Topics in Littlewood-Paley theory and BMO 

    Thompson, Brian (University of Missouri--Columbia, 2012)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this thesis we discuss some important results in Littlewood-Paley theory and the space of Bounded-Mean Oscillation functions, henceforth called BMO. ...
  • Weak Hardy spaces and paraproducts 

    He, Danqing (University of Missouri--Columbia, 2016)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The purpose of this dissertation is to provide a new square function characterization of weak Hardy spaces in the full range of exponents possible and ...