The Selected Papers of Norman Levinson (Google eBook)

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Springer Science & Business Media, 1998 - Mathematics - 536 pages
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The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.
  

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Contents

XII
11
XIII
21
XIV
28
XV
34
XVI
51
XVII
58
XVIII
65
XIX
69
XXXV
230
XXXVI
234
XXXVII
238
XXXVIII
254
XXXIX
266
XL
267
XLI
288
XLII
325

XX
91
XXI
99
XXII
114
XXIII
141
XXIV
152
XXV
155
XXVI
159
XXVII
164
XXVIII
192
XXIX
193
XXX
199
XXXI
203
XXXII
207
XXXIII
211
XXXIV
226
XLIII
333
XLIV
357
XLV
366
XLVI
376
XLVII
384
XLVIII
396
XLIX
415
L
423
LI
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LII
449
LIII
462
LIV
467
LV
494
LVI
505
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