Fast Computation of Volume Potentials by Approximate Approximations

Flavia Lanzara is an associate professor at the Department of Mathematics, University of Rome "La Sapienza" (Italy). Her main research interests are partial differential equations, potential theory, complex analysis, numerical analysis and their applications.Vladimir Maz’ya is a retired Swedish mathematician of worldwide reputation. The author of more than 500 publications, including 20 research monographs, he strongly influenced the development of mathematical analysis and the theory of partial differential equations, as well as the theory of mesoscale asymptotics and numerical analysis.Gunther Schmidt is a retired German mathematician from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin. His main research interests have been approximation theory, theoretical and numerical analysis of integral equation and boundary element methods and their application to electromagnetics and optics.

• Chapter 1. Introduction.- Chapter 2. Quasi-interpolation.- Chapter 3. Approximation of integral operators.- Chapter 4. Some other cubature problems.- Chapter 5. Approximate solution of non-stationary problems.- Chapter 6. Integral operators over hyper-rectangular domains.