Toeplitz operators with semi-almost-periodic matrix symbols on Hardy spaces (Q5945971)

Let \(H^p\), \(1<p<\infty\) be the image of \(L^p (R)\) under the singular projection \(P=\frac 12 (I+S)\), where \(S\) is the Caushy singular integral operator: \((Sf)(x)=(\pi i)^{-1}\int_R (t-x)^{-1}f(t) dt\) on the real line. The authors consider the Toeplitz operators with semi-almost-periodic symbols acting in Hardy spaces \(H^p=PL^p\). They give the Fredholm criteria and the index formula for considered operators under sufficiently general prepositions in compare with earlier known (f.e., \(p=2\) or some additional assumptions about the factorization).