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Selected works. Mathematics. Theoretical physics. Ed. by V. I. Arnol’d. (Избранные труды. Математика. Теоретическая физика.) (Russian) Zbl 0569.01035

Klassiki Nauki. Moskva: Izdatel’stvo “Nauka”. 512 p. R. 3.10 (1984).
Some Russian translations from the work of H. Weyl are published now in the series “The Classicals of the Science”. On behalf of the redaction the book is prefaced by V. I. Arnol’d and A. N. Parshin. Then there follows the translation of 15 memoirs and papers by H. Weyl concerning theoretical physics (the theory of potential, proper oscillations of elastic bodies), (analytic) number theory, foundations of mathematics, differential geometry \((n\)-dimensional spinors, the volume of the tubes), Lie groups (the representation theory of semisimple Lie groups), the theory of invariants, as well as some general philosophical papers (mathematics and logic, the electron and the gravitation, the main features of the physical world). In the completion two other translations are added of the biographical works of H. Weyl on F. Klein and E. Noether.
The book also contains the translation of the paper “Hermann Weyl (1885–1955)” by C. Chevalley and A. Weil [Enseign. Math., II. Sér. 3, 157–187 (1957; Zbl 0078.00412)].
Then a list of the complete works of H. Weyl is given as well as a list of its Russian translations and a bibliography on him. The comments and remarks are largely developed. An index of names and contents conclude the book which is addressed to research workers.
(1) Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers [Rend. Circ. Mat. Palermo 39, 1–50 (1915; JFM 45.1016.02)];
(2) Über die Gleichverteilungen von Zahlen mod Eins [Math. Ann. 77, 313–352 (1916; JFM 46.0278.06)];
(3) Der circulus vitiosus in der heutigen Begründung der Analysis [Jahresber. Deutsch. Math.-Verein. 28, 85–92 (1919; JFM 47.0895.02)];
(4) Theorie der Darstellung Kontinuierlicher halb-einfacher Gruppen durch lineare Transformationen [Math. Z. 23, 271–309 (1925); ibid. 24, 328–376 (1926); ibid. 24, 377–395 (1926); ibid. 24, 789–791 (1926); JFM 51.0319.01];
(5) Elektron und Gravitation [Z. Phys. 56, 330–352 (1929; JFM 55.0513.04];
(6) Eine für die Valenztheorie geeignete Basis der binären Vektorinvarianten (with G. Rumer and E. Teller) [Nachr. Ges. Wiss. Göttingen. Math.-Phys. Kl. 1932, 499–504 (1932; Zbl 0006.14901; JFM 58.0117.02)];
(7) Spinors in \(n\) dimensions (with R. Brauer) [Am. J. Math. 57, No. 2, 425–449 (1935; Zbl 0011.24401; JFM 61.1025.06)];
(8) On the volume of tubes [Am. J. Math. 61, No. 2, 461–472 (1939; Zbl 0021.35503; JFM 65.0796.01)];
(9) The ghost of modality [Philosophical essays in memory of Edmund Husserl, 278–303];
(10) The method of orthogonal projection in potential theory [Duke Math. J. 7, 411–444 (1940; Zbl 0026.02001; JFM 66.0444.01)];
(11) On geometry of numbers [Proc. Lond. Math. Soc. (2) 47, 268–289 (1942; Zbl 0028.34902)];
(12) Mathematics and logic [Am. Math. Mon. 53, 2–13 (1946; Zbl 0060.01904];
(13) Inequalities between the two kinds of eigenvalues of a linear transformation [Proc. Natl. Acad. Sci. USA 35, 408–411 (1949; Zbl 0032.38701)];
(14) The main features of the physical world; morphe and evolution [Philosophy of mathematics and natural science, Appendix F, see pp. 285–301 (Princeton, N.J.: Princeton Univ. Press (1949; Zbl 0033.24209)];
(15) Ramifications, old and new, of the eigenvalue problem [Bull. Am. Math. Soc. 56, 115–139 (1950; Zbl 0041.21003)].
Supplements:
(i) Felix Kleins Stellung in der mathematischen Gegenwart [Naturwissenschaften 18, 4–11 (1930; JFM 56.0026.01)];
(ii) Emmy Noether [Scripta Math. 3, 201–220 (1935; JFM 61.0027.01)] {abridged}.
Reviewer: M. Tarina

MSC:

01A75 Collected or selected works; reprintings or translations of classics
00B55 Collections of translated articles of miscellaneous specific interest