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190748911Paris Gauthier-Villars 1907. 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences" Tome 144 No 11 No. 19 and No. 21. Pp. 593- 664 pp. 1009- 1080. pp. 1137- 1192.3 entire issues offered.Reesz' paper: pp. 615-619. Fischer's paper: pp. 1022-1024 a. 1148-51. Nos 19 a. 21 with some small tears to outher margins. paper fragile. Sewing loose. <br/><br/><em>First apperance of two fundamental papers - Riesz setting forth the theorem and Fischer proving it - the mathematics of which later made it clear that there is an equivalence between matrix mechanics Heisenberg and wave mechanics Schrödinger in quantum physics.The Riesz-Fischer theorem of 1907 concerning the equivalence of the Hilbert space of sequences of convergent sums of squares with the space of functions of summable squares formed the mathematical basis for demonstrating the equivalence of matrix mechanics and wave mechanics. </em> unknown
193148257Easton PA. Mack printing Compagny 1931. Royal8vo. Contemp. full cloth. Spine gilt and with gilt lettering. In: "Proceedings of the National Academy of Sciences of the United States of America" Vol. 17. VII710 pp. Entire volume offered. The papers: pp. 315-318 650-655 and 656-660. <br/><br/><em>First editions of these importent papers in statistical mechanics. The so-called Koopman-von Neumann mechanics is a description of classical mechanics in terms of Hilbert space introduced by Bernard Koopman the paper offered and John von Neumann in 1931 and 1932. Ergodicity was introduced by Boltzmann but the modern theory started from the paper by Koopman and has been a cornerstone of statistical mechanics since. The ergodic method has found impressive applications in the fields of statistical mechanics number theory probability theory harmonic analysis and combinatorics.As Koopman and von Neumann demonstrated a Hilbert space of complex square integrable wavefunctions can be defined in which classical mechanics can be formulated as an operatorial theory similar to quantum mechanics.Birkhoff's proof in the third paper offered of "the ergodic theorem was deemed as importent as his proof of Poincare's geometric theorem" Landmarks Writing in Western Mathematics 1640-1940 p. 877. </em> hardcover