Cubature Formulas & Modern Analysis

In the mid 1960s Academician Sobolev presented a series of lectures at Novosibirsk State Universi@ on the theory of cubature formulas. These new formulas, for calcu in multidimensional space, were named formulas, used to calculate the areas o and updated monograph has.been con lecture notes. After a careful introdu essential in developing the theory of cubature formulas, the author turns to the concept of generalized functions, and discusses the classical problem of approximate integration of functions of several independent variables. Extending Sobolev's studies on formulas for mechanical cubature, the work reveals the diverse relationships between theoretical approximate integration and problems in such areas as mathematical analysis, functional analysis, computational mathematics, and number theory. This introduction to such a vast range of problems will be of value to postgraduates and research workers with a wide-ranging field of interests.