Averaged Wave Operators and Complex-symmetric Operators

作者：Bessonov Roman; Kapustin Vladimir^*

来源：Complex Analysis and Operator Theory, 2016, 10(6): 1213-1226.

DOI：10.1007/s11785-015-0496-1

• Wave operators
• Singular spectral measure
• Cesaro means

We study the behaviour of sequences , where are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator is small in a sense. The conjecture about the weak averaged convergence of the difference to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where is the unitary operator of multiplication by z on , sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.

• 出版日期2016-8