DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION

We study the discretization of inverse problems defined by a Carleman operator. In particular, we develop a discretization strategy for this class of inverse problems and we give a convergence analysis. Learning from examples, as well as the discretization of integral equations, can be analyzed in our setting.

An Integral Representation for the Product of Spectral Measures

Let be a Hilbert space with inner product (•, •) and let E(•) and E0(•) be spectral measures in corresponding to self-adjoint operators and . In this paper we consider the set function ƒ(I × J) = E(I)E0(J) defined on the semiring of bounded rectangles, and obtain an integral representation for this set function for disjoint I, J under the hypotheses that H — H0 is a type of Carleman operator.