Combining Riesz bases

Job Candidate Talk
Thursday, November 13, 2014 - 13:00
1 hour (actually 50 minutes)
Skiles 006
Kent State University
Orthonormal bases (ONB) are used throughout mathematics and its applications. However, in many settings such bases are not easy to come by. For example, it is known that even the union of as few as two intervals may not admit an ONB of exponentials. In cases where there is no ONB, the next best option is a Riesz basis (i.e. the image of an ONB under a bounded invertible operator). In this talk I will discuss the following question: Does every finite union of rectangles in R^d, with edges parallel to the axes, admit a Riesz basis of exponentials? In particular, does every finite union of intervals in R admit such a basis? (This is joint work with Gady Kozma).