Abstract:

Notes by G.N. Keshavamurthy and N.R. Nandakumar. The third of the series 'Concepts in Modern Mathematics' deals with some fundamental concepts in Analysis. The first four chapters comprise the first part. Chapter I gives a detailed description of Lebesgue Integrals. Basic properties of Topological Vector Space are given in chapter 2 while the results are specialized to normed linear spaces in chapter 3 and in particular different Representation Theorems are given. Gelfand theory and elementary properties of Banach Algebras are the contents of Chapter 4. In the remaining chapters which will appear in a separate part, are discussed the existence of Haar integral on a locally compact abelian groups, duality and characters, Fourier Transforms on L1(G) and L2(G) and finally Pontriagin's Duality theorem is proved. Materials are freely drawn from the standard book included in the bibliography given at the end of part 2. 