EAN: 9783642859915

CONTINUOUS TRANSFORMATIONS IN ANALYSIS - TIBOR ...

The general objective of this treatise is to give a systematic presenta­ tion of some of the
topological and measure-theoretical foundations of the theory of real-valued functions of
several real variables  with particular emphasis upon a line of thought initiated by BANACH 
GEOCZE  LEBESGUE  TONELLI  and VITALI. To indicate a basic feature in this line of thought  let
us consider a real-valued continuous function I(u) of the single real variable tt. Such a
function may be thought of as defining a continuous translormation T under which x = 1 (u) is
the image of u. About thirty years ago  BANACH and VITALI observed that the fundamental
concepts of bounded variation  absolute continuity  and derivative admit of fruitful
geometrical descriptions in terms of the transformation T: x = 1 (u) associated with the
function 1 (u). They further noticed that these geometrical descriptions remain meaningful for
a continuous transformation T in Euclidean n-space Rff  where T is given by a system of
equations of the form 1- (1 ff) X-I U  . . .  tt  .   and n is an arbitrary positive integer.
Accordingly  these geometrical descriptions can be used to define  for continuous
transformations in Euclidean n-space Rff  n-dimensional concepts 01 bounded variation and
absolute continuity  and to introduce a generalized Jacobian without reference to partial
derivatives. These ideas were further developed  generalized  and modified by many
mathematicians  and significant applications were made in Calculus of Variations and related
fields along the lines initiated by GEOCZE  LEBESGUE  and TONELLI.

Aktuelle Preise zur EAN 9783642859915

Produktinformationen zur 9783642859915