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.
Author(s): Roger Godement (auth.)
Series: Universitext
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 527
Tags: Real Functions
Front Matter....Pages I-XI
Front Matter....Pages 1-4
The Upper Integral of a Positive Function....Pages 5-19
L p Spaces....Pages 20-36
Measurable Sets and Functions....Pages 37-52
Lebesgue-Fubini’s Way....Pages 53-102
The Lebesgue-Nikodym Theorem....Pages 103-117
Spectral Decomposition on a Hilbert Space....Pages 118-172
The Commutative Fourier Transform....Pages 173-203
Unitary Representations of Locally Compact Groups....Pages 204-259
Front Matter....Pages 261-261
Infinite Series and Products in Number Theory....Pages 261-280
The series \(\sum 1/ {\rm{cos}} \ \pi n z\; {\rm{and}}\; \sum {\rm{exp}} \left(\pi in^2z\right)\) ....Pages 281-297
The Dirichlet Series \(L(s; \mathcal{X})\) ....Pages 298-315
Elliptic Functions....Pages 316-348
SL 2(ℝ) as a Locally Compact Group....Pages 349-375
Modular Functions: The Classical Theory....Pages 376-393
Fuchsian Groups....Pages 394-440
Hecke Theory....Pages 441-462
SL 2(ℝ) as a Lie Group....Pages 463-509
Back Matter....Pages 511-527
