On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Foreign Aid Linked to Infrastructure and/or Pollution Abatement

This paper studies the macroeconomic effects of a permanent increase in foreign aid in a model that takes into account environmental quality. We develop a dynamic equilibrium model in which both public investment in infrastructure and environmental protection can be financed using domestic resources and international aid programs. The framework considers four scenarios for international aid: untied aid,aid fully tied to infrastructure, aid fully tied to abatement, and aid equally tied to both types of expenditures. We find that the effects of the transfers may depend on (i) the structural characteristics of the recipient country (the elasticity of substitution in production and its dependence on environment and natural resources) and on (ii) how recipient countries distribute their public expenditure. These results underscore the importance of these factors when deciding how and to what extent to tie aid to infrastructure and/or pollution abatement.