2023/01/26 by Dorin Ervin Dutkay, Dutkay, Dorin Ervin, Palle E. T. Jørgensen +1 · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2301.11377
The purpose of the present paper is to place a number of geometric (and hands-on) configurations relating to spectrum and geometry inside a general framework for the \it Fuglede conjecture. Note that in its general form, the Fuglede conjecture concerns general Borel sets Ω in a fixed number of dimensions d such that Ω has finite positive Lebesgue measure. The conjecture proposes a correspondence between two properties for Ω, one takes the form of spectrum, while the other refers to a translation-tiling property. We focus here on the case of dimension one, and the connections between the Fuglede conjecture and properties of the self-adjoint extensions of the momentum operator (1)/(2πi)(d)/(dx), realized in L2 of a union of intervals.