Codes and Expansions (CodEx) Seminar

Ilya Krishtal (Northern Illinois University):
Kadec-type theorems for unit-norm frames and atomic decompositions

In 1964 Kadec established the exact value of the Paley-Wiener constant which bounds the perturbation of harmonics in the orthonormal basis of exponential functions for the system to remain a Riesz basis. The result has many extensions such as the theorems by Katznelson, Avdonin, and Balan. All of these extensions, however, apply to systems of exponential functions on an interval. In this talk, I will show how to extend Kadec’s proof to systems of vectors generated by sampling an orbit of a vector under an isometric group representation. The talk is based on joint work with B. Miller.