Tensile behavior of nickel foam/polyurethane co-continuous composites

junxiang wang, deli duan, xiaoguang yang, mingyang li, shu li
2019 Materials Research Express  
To construct dual frames with good structure for a given frame is a fundamental problem in the theory of frames. The tensor product duals of tensor product frames can provide a rank-one decomposition of bounded antilinear operators between two Hilbert spaces. This paper addresses tensor product dual frames. We derive a necessary and sufficient condition for two tensor product Bessel sequences to be a pair of dual frames; obtain explicit expressions of all dual frames and tensor product dual
more » ... or product dual frames of tensor product frames; and demonstrate the existence of non-tensor product dual frames of tensor product frames. MSC: Primary 42C15; secondary 41A58; 47A80
doi:10.1088/2053-1591/ab2f9d fatcat:mz3qkalfbbbwhl6hgqyffiiafu