Abstract
Truncated correlation and convolution operators is a general operator-class containing popular operators such as Toeplitz (Wiener–Hopf), Hankel and finite interval convolution operators as well as small and big Hankel operators in several variables. We completely characterize the symbols for which such operators have finite rank, and develop methods for determining the rank in concrete cases. Such results are well known for the one-dimensional objects, the first discovered by L. Kronecker during the nineteenth century. We show that the results for the multidimensional case differ in various key aspects.
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Andersson, F., Carlsson, M. On General Domain Truncated Correlation and Convolution Operators with Finite Rank. Integr. Equ. Oper. Theory 82, 339–370 (2015). https://doi.org/10.1007/s00020-015-2217-6
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DOI: https://doi.org/10.1007/s00020-015-2217-6