(Semi)-Fredholmness of convolution operators on the spaces of Bessel potentials. (English) Zbl 0809.45004
Basor, E. L. (ed.) et al., Toeplitz operators and related topics. The Harold Widom anniversary volume. Workshop on Toeplitz and Wiener-Hopf operators, Santa Cruz, CA, USA, September 20-22, 1992. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 71, 122-152 (1994).
Summary: The consideration of above mentioned operators on the union of intervals and/or rays is reduced to the canonical situation of operators \(W_ K\) on \(L_ p (\mathbb{R}_ +)\) with semi almost periodic presymbols \(K\) at the expense of inflating the size of \(K\). The Fredholm theory (that is, conditions of \(n\)-, \(d\)-normality and the index formula) is developed. In particular, relations between (semi-) Fredholmness of \(W_ K\), invertibility of \(W_{K_ \pm}\) with \(K_ \pm\) being almost periodic representatives of \(K\) at \(\pm \infty\), and factorability of \(K_ \pm\) are established.
For the entire collection see [Zbl 0797.00014].
For the entire collection see [Zbl 0797.00014].
MSC:
45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
47A53 | (Semi-) Fredholm operators; index theories |
47A68 | Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators |