• Frames and projections 

    Cahill, Jameson (University of Missouri--Columbia, 2013)
    In this dissertation we explore several ways in which the concept of projections arise infinite frame theory. In the first chapter we show that the Paulsen problem from frame theory is equivalent to a long standing open ...
  • Fusion frame constructions and frame partitions 

    Peterson, Jesse D. (University of Missouri--Columbia, 2013)
    Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Despite ...
  • Limit of many molecules dynamics with rigorous macroscopic results 

    Jacob, Nicholas C. (University of Missouri--Columbia, 2013)
    The thesis builds on recent ideas that combine work by C.B. Morrey (1955) and D.W. Jepsen & D. ter Haar (1962) with more recent analytic techniques: measure disintegration, PDEs for measures, etc. (M.I. Vishik & A.V. ...
  • Stability estimates for semigroups and partly parabolic reaction diffusion equations 

    Yurov, Valerian (University of Missouri--Columbia, 2013)
    The purpose of my dissertation is the application of the methods of abstract theory of strongly continuous operator semigroups (and of evolution semigroups in particular) to study of the spectral properties of a class of ...
  • Stochastically perturbed Navier-Stokes system on the rotating sphere 

    Varner, Gregory Alan (University of Missouri--Columbia, 2013)
    We show the existence and uniqueness of an invariant measure for the kick-forced Navier-Stokes system on the 2-dimensional sphere, first without deterministic force and then with a time-independent deterministic force. The ...