Analysis Volume IV introduces the reader to functional analysis (integration Hilbert spaces
harmonic analysis in group theory) and to the methods of the theory of modular functions (theta
and L series elliptic functions use of the Lie algebra of SL2). As in volumes I to III the
inimitable style of the author is recognizable here too not only because of his refusal to
write in the compact style used nowadays in many textbooks. The first part (Integration) a
wise combination of mathematics said to be `modern' and `classical' is universally useful
whereas the second part leads the reader towards a very active and specialized field of
research with possibly broad generalizations.
