This is off-topic: But powerful techniques to show that gap exist, can be found in the following papers:

Link

Link

of course. The setting is somewhat different, since they consider discrete Schroedinger operators ...

This is off-topic: But powerful techniques to show that gap exist, can be found in the following papers:

• Michael Goldstein, Wilhelm Schlag, On resonances and the formation of gaps in the spectrum of quasi-periodic Schroedinger equations

• Artur Avila, Jairo Bochi, David Damanik, Opening Gaps in the Spectrum of Strictly Ergodic Schrödinger Operators

of course. The setting is somewhat different, since they consider discrete Schroedinger operators ...

This is off-topic: But powerful techniques to show that gap exist, can be found in the following papers:

http://front.math.ucdavis.edu/0511.5392

http://front.math.ucdavis.edu/0903.2281

of course. The setting is somewhat different, since they consider discrete Schroedinger operators ...

This is off-topic: But powerful techniques to show that gap exist, can be found in the following papers:

Link

Link

of course. The setting is somewhat different, since they consider discrete Schroedinger operators ...