History of Functional Analysis

Cover......Page 1
Title page......Page 3
Date-line......Page 4
TABLE OF CONTENTS......Page 5
INTRODUCTION......Page 7
1. Differential equations and partial differential equations in the XVIII-th century......Page 15
2. Fourier expansions......Page 17
3. The Sturm-Liouville theory......Page 22
1. The method of successive approximations......Page 28
2. Partial differential equations in the XIX-th century......Page 32
3. The beginnings of potential theory......Page 36
4. The Dirichlet principle......Page 41
5. The Beer-Neumann method......Page 45
1. H.A. Schwarz\'s 1885 paper......Page 53
2. The contributions of Poincare......Page 62
1. Linear algebra in the XIX century......Page 77
2. Infinite determinants......Page 81
3. Groping towards function spaces......Page 85
4. The passage \"from finiteness to infinity\"......Page 93
1. Fredholm\'s discovery......Page 103
2. The contributions of Hilbert......Page 111
3. The confluence of Geometry, Topology and Analysis......Page 121
1. The search for continuous linear functionals......Page 127
2. The $L^p$ and $l^p$ spaces......Page 130
3. The birth of normed spaces and the Hahn-Banach theorem......Page 134
4. The method of the gliding hump and Baire category......Page 144
1. F. Riesz\'s theory of compact operators......Page 150
2. The spectral theory of Hilbert......Page 154
3. The work of Weyl and Carleman......Page 166
4. The spectral theory of von Neumann......Page 177
5. Banach algebras......Page 188
6. Later developments......Page 196
1. Weak convergence and weak topology......Page 216
2. Locally convex spaces......Page 221
3. The theory of distributions......Page 227
1. Fixed point theorems......Page 239
2. Carleman operators and generalized eigenvectors......Page 244
3. Boundary problems for ordinary differential equations......Page 249
4. Sobolev spaces and a priori inequalities......Page 254
5. Elementary solutions, parametrices and pseudo-differential operators......Page 258
REFERENCES......Page 286
AUTHOR INDEX......Page 305
SUBJECT INDEX......Page 312