The current of the bc-system of higher rank introduced recently is examined. Its one-point function is described geometrically and some local computations for the operator product expansions are made.

We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block rank. We cover in particular the data-space format of H-matrices. We show the approximability result for two types of discretizations. The first one is a saddl...

A general result on the structure and dimension of the root subspaces of a linear operator under finite rank perturbations is proved: The increase of dimension from the n-th power of the kernel of the perturbed operator to the (n+ 1)-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation. Thi...

For a separable complex Hilbert space H, we say that bounded linear operator T acting on H is C-normal, where C conjugation if it satisfies CT∗TC=TT∗. normal operator, give geometric conditions which guarantee its rank-one perturbation C-normal for some C. We also obtain new properties revealing the structure of operators.

an l-fuzzifying matroid is a pair (e, i), where i is a map from2e to l satisfying three axioms. in this paper, the notion of closure operatorsin matroid theory is generalized to an l-fuzzy setting and called l-fuzzifyingclosure operators. it is proved that there exists a one-to-one correspondencebetween l-fuzzifying matroids and their l-fuzzifying closure operators.