Spectral property of Cantor measures with consecutive digits

Spectrality of a class of infinite convolutions

“…In another direction, Jorgensen and Pedersen [16] made a head start to study the spectral property of the self-similar measures. Nowadays, there is a large literature on this topic [1][2][3][4][5][6][7]9,[12][13][14][15][16][19][20][21][23][24][25][26][28][29][30]. Among those, one of the best known results is that if ρ = 1/q for some integer q > 1, then μ ρ,{0,1} is a spectral measure if and only if q is an even integer [16].…”

“…If all (b k , D k ) are admissible, there are various methods to construct an infinite set Λ such that E Λ is an orthonormal set of L 2 (μ {b k }, {D k } ) [1,3,6,16,21,23,28,29]. In general the difficult part is to verify the completeness of E Λ .…”

Spectrality of the planar Sierpinski family

“…For example, in 1998 Jorgensen and Pedersen [16] found the first singular, non-atomic, self-similar spectral measure supported on 1 4 -Cantor set. Nowadays, there is a large literature on this topic [1][2][3][4][5][6][7][8]10,[13][14][15][16]19,20,26,28,29,31]. Most of this literature deals with the issue in one dimension.…”

Spectral property of a class of Moran measures on R

“…In recent years, there has been a wide range of interests in expanding the classical Fourier analysis to fractal or more general probability measures after the pioneer work of Jorgensen and Pedersen [16] in 1998 [1][2][3][4][5][6][7][9][10][11]14,15,[19][20][21][22][23][24][27][28][29]31]. One of the central themes of this area of research involves constructing Fourier bases in L 2 (μ), where μ is a measure which is generated by the iterated function systems.…”