Approximation numbers and approximation of the eigenvalues of integral operators (Q1101931)

Let \(X=L_ 2[0,2\pi]\), and h(x,y) be a kernel generating an operator H in X. Then \(\partial h\) j/\(\partial y\) j defines an operator \(H_ j\) and \(\partial\) \(iH_ j/\partial x_ i\) is required to be a continuous operator. Finite rank operators are constructed such that their eigenvalues approximate the spectrum of H. Additionally, quantitative estimates of the approximation are also obtained.