Our Colloquium series offers a diverse platform for research scholars, faculty, students, and industry experts to share and exchange ideas, fostering discussion and networking across mathematics, statistics, and data science.
Dr. Thibaud Alemany (University of Central Florida) will speak at this week's colloquium on "Geometric properties of reproducing kernels in linear model spaces."
Abstract: Linear meromorphic model spaces are closed subspaces of the Hardy space that consist of meromorphic functions analytic through the real line. We consider systems of reproducing kernels $K(\Lambda)$ where $\Lambda$ is a subset of $\R$. We derive necessary and sufficient conditions for the system $K(\Lambda)$ to be a Riesz basis, frame, Riesz sequence or Bessel system. We show that these systems are closed under some perturbations and derive sufficient conditions in terms of the density of the set $\Lambda$ for the system to be a Riesz sequence or a frame.
Speaker Bio: Dr. Thibaud Alemany is a Post Doctoral Associate in the Department of Mathematics at the University of Central Florida. He earned his PhD in Mathematics from the Georgia Institute of Technology under the supervision of Michael Lacey. Dr Alemany's research encompass harmonic analysis, complex analysis, functional analysis, basis theory, interpolation and sampling in reproducing kernel Hilbert spaces.
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