clopen.solutions

Open problems

980 registered problems.

OP-00021 Open
Interior of the spectrum of the boat–star tiling Laplacian
SP · aperiodic order · Cantor spectrum · graph Laplacian · Penrose tiling
OP-00022 Open
Intervals of spectrum at the edges of the boat–star tiling spectrum
SP · aperiodic order · graph Laplacian · Penrose tiling · spectral edges
OP-00023 Open
Closed form for the top of the boat–star tiling spectrum
SP · aperiodic order · graph Laplacian · Penrose tiling · spectral edges
OP-00024 Open
Tilings without locally supported eigenfunctions in every MLD class
SP · aperiodic order · graph Laplacian · locally supported eigenfunctions · mutual local derivability
OP-00025 Open
Finitely many jumps in the integrated density of states of a linearly repetitive tiling
SP · aperiodic order · graph Laplacian · integrated density of states · linear repetitivity · locally supported eigenfunctions
OP-00026 Open
Hölder continuity of the boat–star integrated density of states at the spectral edges
SP · aperiodic order · Hölder continuity · integrated density of states · Penrose tiling · spectral edges
OP-00787 Solution claimed
Characterizing discrete sets generated by fixed-parameter extrapolation
MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · Pisot numbers
OP-00788 Solution claimed
Relative density of sets generated by fixed-parameter extrapolation
MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · relatively dense sets