2011/11/18 by Palle E. T. Jørgensen, Jorgensen, Palle E. T., Keri Kornelson +3
Mathematics · #42A #46E #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1111.4487
openalex publication_date 2011/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Each Cantor measure (μ) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L2(μ). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L2(μ), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB (Γ) is the original Jorgensen-Pedersen ONB for the Cantor measure (μ) and the other ONB is is 5Γ. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.