# Continuous Spectrum or Measurable Reducibility for Quasiperiodic Cocycles in $${\mathbb{T} ^{d} \times SU(2)}$$Td×SU(2)

@article{Karaliolios2015ContinuousSO, title={Continuous Spectrum or Measurable Reducibility for Quasiperiodic Cocycles in \$\$\{\mathbb\{T\} ^\{d\} \times SU(2)\}\$\$Td×SU(2)}, author={Nikolaos Karaliolios}, journal={Communications in Mathematical Physics}, year={2015}, volume={358}, pages={741-766} }

AbstractWe continue our study of the local theory for quasiperiodic cocycles in $${\mathbb{T} ^{d} \times G}$$Td×G , where $${G=SU(2)}$$G=SU(2) , over a rotation satisfying a Diophantine condition and satisfying a closeness-to-constants condition, by proving a dichotomy between measurable reducibility (and therefore pure point spectrum), and purely continuous spectrum in the space orthogonal to $${L^{2}(\mathbb{T} ^{d}) \hookrightarrow L^{2}(\mathbb{T} ^{d}
\times G)}$$L2(Td)↪L2(Td×G… Expand

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