Fuglede's tiling-spectrality conjecture
Which domains in Euclidean space admit an orthogonal basis of exponential functions? For example, the cube is such a domain, but the ball is not. In 1974, Fuglede made a fascinating conjecture that these domains could be characterized geometrically as the domains which can tile the space by translations. I will survey the subject and report about the recent developments on Fuglede's conjecture.
תאריך עדכון אחרון : 08/12/2019