Gaps Spectrum Potential Theory References

The lecture title is a bit of a misnomer in that we'll mainly discuss whole line periodic Jacobi matrices although the half-line objects will enter a lot in future lectures. So {an, bn}∞n=− ∞ are two-sided sequences with some p> 0 in Z so that an+p = an bn+p = bn For z ∈ C fixed, we are interested in solutions {un}∞n=0 of anun+1 + bnun + an−1un−1 = zun Floquet Solution