S.G. Mikhlin

The present monograph has points in common with two branches of analysis. One of them is the variational-difference method (the finite element method), the other is the constructive theory of functions. The starting point is the construction of special classes of coordinate functions for the variational-difference method. It is based on elementary transformations .of the independent variables of given "primitive" functions. After the construction of the coordinate functions, the next step is to approximate functions of a given class by linear combinations of the coordinate functions, and to derive in some appropriate norm an estimate of the error. Clearly, this is a problem closely connected with the constructive theory of functions. The monograph contains 11 chapters. Chapter I discusses Courant's basic idea which is central to the construction of variational-difference methods. One of Courant's examples, from which the notion of a primitive function follows naturally, is examined in some detail. The general definition of a primitive function and the method of construction for the corresponding coordinate functions are given and discussed. Chapters II-VI are more closely connected with the constructive theory of functions. The completeness of the coordinate systems defined in Chapter I are studied, as well as the order of approximation obtained through the use of linear combinations of these functions. Their completeness in Sobolev spaces are examined in Chapter II, while related orders of approximation are derived in Chapter III.

In the twentieth century few societies have vacillated between extremes on the death penalty as has Russia. Taking the century as a whole, few countries have used capital punishment so massively, whether judicially or extrajudicially. Dr. Mikhlin's study is an invaluable contribution to this debate. He offers statistics, official and unofficial, on the death penalty which inform the discussion, but more importantly, he addresses issues which have been largely ignored, even in the specialist literature. These include an examination of the purposes of chastisement in the form of capital punishment and the internal procedures followed with respect to pardons, as well as the regimes under which prisoners are confined and the theories of punishment responsible for the configuration of these regimes. He explores the legal status of persons sentenced to death and, on a comparative basis, the means by which the sentence is carried out. The work is intended for scholars, students, postgraduates, and those who work in agencies which execute punishments, the courts and the Ministry of Justice, as well as for the general reader with an interest in the issue of the death penalty.

Keine ausf hrliche Beschreibung f r "Singular Integral Operators" verf gbar.