Analytical solution of a new class of integral equations. (Q1413566)

The author gives an algorithm for finding analytically the unique solution \(h\in H^{-\alpha}(0,L)\) to the following equation \(Rh= f\), where \(Rh= \int^L_0 R(x,y) h(y)\,dy\), and the kernel \(R(x,y)\) satisfies the equation \(QR= P\delta(x-y)\), \(0\leq x\leq L\). The above equation is the basic equation of random processes estimation theory. Finally, generalizations of the above equation in the multidimensional case are also considered.