Research

More precisely, recent interests include the following overlapping topics:

  • Quantum Graphs are differential operators on metric graphs, which exhibit features of both ordinary and partial differential operators. Of particular interest is the relation of geometric properties of the graph with spectral properties of the operator.
  • Another class of operators of interest are (linear and multilinear) Fourier integral and Pseudodifferential operators, for which in particular boundedness is investigated.
  • Within singular problems we focus on both on differential operators with strongly singular potentials as well as more abstractly super singular perturbations of self-adjoint operators.
  • Beside direct spectral and scattering problems also Inverse Problems are considered, in particular for quantum graphs as well as with problem related to tomography.
  • In complex analysis we are working on different topics related to functions of several variables, including integral representations for Herglotz-Nevanlinna functions and boundary behavior and integrability questions for bounded functions on polydisks.
  • The study of Banach spaces of analytic functions, such as Hardy, Bergman, and Dirichlet spaces, and their operators, also involves heavy use of complex analysis. The main interest here is to identify cyclic vectors and analyze the structure of invariant subspaces for shift operators.
  • Conformal mapping models of Laplacian growth and other conformal proesses are studied using a combination of complex-analytic methods, such as Loewner's differential equation, and methods from probability theory and stochastic analysis.

Seminars

Our seminar is usually on Wednesday mornings Analys, write an email to luger (at) math.su.se if you want to get a reminder each week.

Members