Invertibility Issues for Toeplitz Plus Hankel Operators and Their Close Relatives

The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and lp-spaces, integral difference Wiener-Hopf generalized operators. Special attention is paid a newly developed method, which allows establish necessary, sufficient also necessary conditions invertibility, one-sided for wide classes derive efficient formulas corresponding inverses. work contains number problems whose solution would be interest both theoretical applied contexts.