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BARRY SIMON'S Online Selecta

Often  mathematicians had complete works published, usually after they are complete.  These are especially valuable when, as for example with Askey in Szegő's complete works, they include commentary on some or all of the papers.  More recently, there has arisen a tradition of Selecta -- not complete works but the most important, often published while the author is still alive.  Added value here is that the commentary can be by the author and, in some cases, there are charming autobiographical notes as in Dyson's Selecta.

During my career, there has been a revolution in the mechanics of dissemination of mathematical research.  (I note parenthetically that there are stories from the early fifties of lost paper manuscripts and book drafts that needed to be rewritten from scratch in the pre-Xerox era.  When I started Xeroxing was so expensive that one produced preprints by having a secretary produce green mimeograph stencils.  They typed with the keys making holes in the green sheets and afterwards a mimeograph machine forced ink through the holes.  The first round of proofreading was done by the secretary placing a sheet of paper behind the stencil.  Corrections where done by using a special fluid to cover up holes and retyping.  The only way to do the second round of proofreading was to hold the stencils up to the light and go crazy.)  In particular, papers are now so readily available online that I have all my papers (and so an updated complete works) available online at this site. 

Printed Selecta by this point in time seem to be an exercise in wasted paper and ego fulfillment!  But since the commentary can be useful, I've decided to provide that online in downloadable .pdf files.  This is a work in progress.  When a pdf exists, there is dark text and a hyperlink.  When not, the text is grey, so I can indicate my somewhat ambitious plans.  I begin with a list of what I regard as my top fifteen "papers" (in quotes since most represent several actual papers), then a list of biographical notes and finally commentary on collections of papers by topic, more or less in chronological order.  This commentary is a mix of notes on the history of the papers and on some of the later developments.  The numbers in brackets are from the paper list.  I expect that fleshing out this project will take several years.  If you have comments including typos, please email me.

Note: These commentaries are a work in progress.  Cross references to comments that remain to be written will appear as [TK].

Top Fifteen Results

Biographical Notes
  1. Forebears and Youth
  2. College and Grad School
  3. Princeton in the 70's
  4. Caltech
  5. Computer Journalism
  6. Math Wars
  7. Torah Codes
Selecta
  1. Quadratic Form Techniques [I, 13, 81, 82, 96, 98, 116]
  2. Singular Eigenvalue Perturbation Theory [6, 7, 10, 11, VII, i, ii, v, xxiii, 17, 19, 20, 28, 70, 72, 80, 100, 101, 102, 104, 105, 111, 115, 122, 136, 156, 161, 162, 163, 174, 177, 219, xxiii, xxxi, xxxvi]
  3. Single Particle NRQM [I, X, 5, 24, 35, 38, 59, 71, 99, 110, 114, 115, 135, 137, 157, 165, 179, 181, 200, 203, 208, 210, 215, 226, 227, 229, 253, 254, 256, 269, 276, 293, 295, 320, 321, 322, 326, 331, 335, IX, x, xvi, xxi, xxii, xxv, xxviii, xxxix, xlii]
  4. Multiparticle NRQM [X, 9, 27, 39, 44, 83, 85, 119, 120, 122, x, xxi, xxiv, xxxi, xxxix]
  5. Reed-Simon [II, III, V, VII]
  6. Assorted Functional Analysis [12, 14, 29, 30, 36, 41, 73, 74, 103, 109, 116, 135, 137, 138, 140, 142, 145, 150, 186, 196, 209, 220, 222, 223, 270, 325, 326, 328, II, VIII, iv]
  7. Spectral Reflection Coefficient [99, 326]
  8. Hyercontractivity and all that [16, 24, 69, 173, 186, xxix, xxxiv]
  9. Constructive QFT [16, 18, 21, 23, 31, 32, 33, 34, 37, 40, 47, IV, 48, 49, 50, 60, 61, 62, 63, 77,  153, iii, v, vi, vii, viii, ix]
  10. Complex Scaling [25, 26, 44, 107, 121, xv]
  11. Statistical Mechanical Methods in QFT [32, 33, 34, 37, 40, 47, 48, 49, 50, IV, vii, viii, ix]
  12. Quasiclassical limits and bounds (including Thomas Fermi) [39, 45, 53, 55, 73, xxxvii]
  13. Bargmann Festschrift Reviews [xi, xii]
  14. Nonabelian symmetry breaking in Statistical Mechanics [64, 65, 67, 68, xiv]
  15. Statistical Mechanics, especially of Lattice Gases [XI, 57, 58, 64, 65, 67, 68, 93, 94, 112, 113, 118, 127, 128, 129, 139, 143, 144, xiii, xiv, xvii, xviii]
  16. Exponential Decay of Quantum Wave Functions [43, 46, 51, 95, 133, 134, xxi]
  17. Diamagnetic Inequality [66, 76, 86, 117, 286]
  18. Trace Ideal Methods and Book [VIII, 60, 73, 74, 138, 140]
  19. Functional Integration Book [IX, 135, 274, xix, xx, xxi]
  20. Magnetic Fields [38, 87, 88, 89, 90, 91, 92, 117, 130, 151, 183, 199]
  21. Periodic Schrödiner Operators [X, 75, 79, 141, 179, 337]
  22. Geometric Methods, Enss and Moore Theory [X, 84, 106, 124, 125, 131, 132, 135, xxii]
  23. Atomic and Molecular Physics [X, 97, 107, 108, 119, 120, 121, 160, 175]
  24. Foundations of Ergodic Schrodinger Operators [X, 142, 146, 147, 148, 149, 152, 155, 164, 166, 167, 168, 169, 170, 176, 178, 182, 187, 188, 189, 190, 192, 194, 198, 207, 211, 218, 231, 232, 236, 250, 251, 257, 263, 265, 324, xxvi, xxx, xxxii, xxxiii, xxxiv]
  25. Bayreuth Lectures and Schrödiger Semigroups [X, xxi]
  26. Nonclassical eigenvalue asymptotics, Cusps and Strange Domains [158, 159, 212, 217, 221, 225]
  27. Lifshitz tails [180, 191, xxxii]
  28. Simon-Taylor Method [187, 188]
  29. Simon-Wolff Criterion [187, 189, 190, 192]
  30. Bundle Fibrosis [X, 171, 172, 197, 204, 205, 216, 228]
  31. Operators with singular continuous spectrum [233, 234, 235, 236, 242, 243, 245, 246, 247, 248, 250, 251]
  32. Rank One Perturbations [189, 235, 238, 242, 244, 250, 251, 308, VIIIa, xxxviii]
  33. Last-Simon and Kiselev-Last-Simon [263, 265, 267, 279]
  34. New Approach to Inverse Spectral Theory [271, 272, 273]
  35. Other Inverse Problems [230, 237, 239, 240, 241, 243, 249, 252, 258, 259, 260, 261, 264, 266, 268, 275, 289]
  36. Krein Spectral Shift [262, 277, 314]
  37. Spectral Theory Methods in Orthogonal Polynomials (including OPUC Book) [XIII, XIV, XV, 280, 281, 282, 283, 284, 285, 287, 288, 290, 291, 292, 294, 296, 297, 301, 302, 303, 305, 307, 308, 310, 311, 312, 317, 318, 319, 323, 324, 327, 329, 330, 332, 333, 334, xliii, xliv, xlvi, xlvii, xlviii, li, lii, lv]
  38. Killip-Simon and DKS [280, 281, 282, 288, 306, 312, XV, lv]
  39. Damanik Simon on Szegő  asymptotics [301]
  40. Fine Structure of Zeros [298, 299, 300, 309, 324, xlix, liv]
  41. Ultimate HVZ theorems [84, 263, 304]
  42. Eigenvalue Bounds of Lieb Thirring Type [280, 313, 315, 329]
  43. Lubinsky's Theorem [316, 324]
  44. CSZ on Finite Gaps [323, 327, 329, 332, XV, l, lvi]
  45. Porter Lectures [XV]
  46. Group Rep and Convexity Books [XII, XVI]
  47. Comprehensive Course [XVII, XVIII, XIX, XX, XXI]
  48. Chebyshev Polynomials [336]
  49. Large Deviations
  50. Loewner's Theorem on Monotone Matrix Functions
  51. Problem Lists [xxvii, xl]