ANALYSIS  SEMINAR (UTK)

Abstract: I recently introduced the concept of pseudo-Riesz bases, extending the influential idea of near-Riesz bases first proposed by J. Holub in the 1990s. I established that pseudo-Riesz bases can be characterized as sequences with a Fredholm synthesis operator. Unlike Riesz bases, they are neither spanning nor independent, yet they retain valuable expansion properties. I have also developed some perturbation results for our Pseudo-Riesz bases.A well-known result by Hrusˇcˇev, Nikol’ski ̆i, and Pavlov characterizes Riesz bases of non-harmonic complex exponentials in terms of the invertibility of an appropriate Toeplitz operator. I prove a similar result for pseudo-Riesz bases of non-harmonic complex exponentials, aiming to establish Kadec-type perturbation results.