Analysis Seminar

• November 2, 2022
• 11:00 AM - 12:00 CST
• BVM 506
• Rafal Goebel, rgoebel1@luc.edu
• Open to the public.
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• Details

  Speaker:

  Xiang Wan, Loyola University Chicago

  
  Title:

  Operator Semigroups and Applications to Differential Equations, Part I

  Abstract:

  Many differential equations have the abstract form x¿(t) = Ax(t) + f(t). Indeed, A being a number gives an ODE; A being a matrix corresponds to an ODE system (finite dimensional); A being an operator leads to, generally, a PDE (infinite dimensional). While the first two cases are well understood, the last case is vastly more complicated due to the operator A being unbounded in general. For instance, when A being a Laplacian, we are looking at the heat equation.

  In this first talk, we will closely examine the case when A is a matrix or a bounded operator. In particular, the spectral decomposition reveals a deeper connection with the unbouded case, which will be discussed in following talks.