Advertisement

Some views on the evolution of harmonic analysis

  • Jean-Paul Pier
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1359)

Keywords

Invariant Measure Topological Group Compact Group Unitary Representation Banach Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ambrose, Warren. Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57, 364–386 (1945).MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Bochner, Salomon. Vorlesungen über Fouriersche Integrale. Akademie Verlagsgesellschaft, Leipzig, 1932.zbMATHGoogle Scholar
  3. [3]
    Bochner, Salomon. Monotone Funktionen, Stieltjessche Integrale. und harmonische Analyse. Math. Ann. 108, 378–410 (1933).MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Bohr, Harald. Sur les fonctions presque périodiques. C. R. Acad. Sci. Paris 177, 737–739 (1923).zbMATHGoogle Scholar
  5. [5]
    Bourbaki, Nicolas. Intégration. Chapitres 7,8. Hermann, Paris, 1963.Google Scholar
  6. [6]
    Burkhardt, H. Trigonometrische Reihen und Integrale (bis etwa 1850), 1914. Enzyklopädie der Wissenschaften, volume II, 825–1353. Teubner, Berlin, 1916.Google Scholar
  7. [7]
    Cartan, Henri, and Roger Godement. Théorie de la dualité et analyse harmonique dans les groupes abéliens localement compacts. Ann. Sci. Ecole Norm. Sup. 64, 79–99 (1947).MathSciNetzbMATHGoogle Scholar
  8. [8]
    Chevalley, Claude. Génération d'un groupe topologique par des transformations infinitésimales. C. R. Acad. Sci. Paris 196, 744–746 (1933).zbMATHGoogle Scholar
  9. [9]
    Connes, Alain. Classification of injective factors. Ann. of Math. 104, 73–115 (1976).MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Dantzig, D. van. Zur topologischen Algebra I. Math. Ann. 107, 587–626 (1932).MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Derighetti, Antoine. Relations entre les convoluteurs d'un groupe localement compact et ceux d'un sous-groupe fermé. Bull. Sci. Math. 106, 69–84 (1982).MathSciNetzbMATHGoogle Scholar
  12. [12]
    Derighetti, Antoine. A propos des convoluteurs d'un groupe quotient. Bull. Sci. Math. 107, 3–23 (1983).MathSciNetzbMATHGoogle Scholar
  13. [13]
    Dirichlet, Gustav Peter Legeune. Sur la convergence de séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données. J. Reine Angew. Math. 4, 157–169 (1829).MathSciNetCrossRefGoogle Scholar
  14. [14]
    Ditkin, V. A. Study of the structure of ideals in certain normed rings (in Russian). Ucenye Zapiski Moskov. Gos. Univ. Matematika 30, 83–130 (1939).MathSciNetGoogle Scholar
  15. [15]
    Eymard, Pierre. L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France 92, 181–236 (1964).MathSciNetzbMATHGoogle Scholar
  16. [16]
    Eymard, Pierre. Algèbres Ap et convoluteurs de Lp(G). Séminiare Bourbaki, Vol. 1969/70. Lecture Notes in Mathematics, Vol. 180, 364–381. Springer Verlag, Berlin, 1971.Google Scholar
  17. [17]
    Fischer, Ernest. Sur la convergence en moyenne. C. R. Acad. Sci. Paris 144, 1022–1024 (1907).zbMATHGoogle Scholar
  18. [18]
    Fourier, Joseph. Théorie analytique de la chaleur. Didot, Paris, 1822.zbMATHGoogle Scholar
  19. [19]
    Fourier, Joseph. Oeuvres. Volume I, 1888. Gauthier-Villars, Paris.zbMATHGoogle Scholar
  20. [20]
    Freudenthal, Hans. Einige Sätze über topologische Gruppen. Ann. of Math. 37, 46–56 (1936).MathSciNetzbMATHCrossRefGoogle Scholar
  21. [21]
    Gelfand, I. M. Normierte Ringe. Mat. Sb. 9, 3–24 (1941).MathSciNetzbMATHGoogle Scholar
  22. [22]
    Gelfand, I. M., and D. A. Raikov. Irreducible unitary representations of locally bicompact groups. Mat. Sb. 13, 301–316 (1943). Amer. Math. Soc. Transl. 36, 1–15 (1964).MathSciNetzbMATHGoogle Scholar
  23. [23]
    Godement, Roger. Théorèmes taubériens et théorie spectrale. Ann. sci. Ecole Norm. Sup. 64, 119–138 (1947).MathSciNetzbMATHGoogle Scholar
  24. [24]
    Godement, Roger. Les fonctions de type positif et la théorie des groupes. Trans. Amer. Math. Soc. 63, 1–84 (1948).MathSciNetzbMATHGoogle Scholar
  25. [25]
    Granirer, Edmond E. Density theorems for some linear subspaces and some C*-subalgebras of VN(G). Symposia Mathematica XXII. Analisi armonica e spazi di funzioni su gruppi localmente compatti, 61–70. Academia, New York, 1977.Google Scholar
  26. [26]
    Haar, Alfred. Der Massbegriff in der Theorie der kontinuierlichen Gruppen. Ann. of Math. 34, 147–169 (1933).MathSciNetzbMATHCrossRefGoogle Scholar
  27. [27]
    Herz, Carl. Harmonic synthesis for subgroups. Ann. Inst. Fourier (Grenoble) XXIII, 3, 91–123 (1973).MathSciNetzbMATHCrossRefGoogle Scholar
  28. [28]
    Hilbert, David. Mathematische Probleme. Akad. Wiss. Göttingen, Göttingen, 253–297 (1900).Google Scholar
  29. [29]
    Hurwitz, Adolf. Ueber die Erzeugung der Invarianten durch Integration. Göttingen Nachrichten 71–90 (1897).Google Scholar
  30. [30]
    Iwasawa, Kenkishi. On some types of topological groups. Ann. of Math. 50, 507–558 (1949).MathSciNetzbMATHCrossRefGoogle Scholar
  31. [31]
    Johnson, Barry. An introduction to the theory of centralizers. J. London Math. Soc. 14, 229–320 (1964).MathSciNetGoogle Scholar
  32. [32]
    Johnson, Barry. Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127 (1972).Google Scholar
  33. [33]
    Kahane, Jean-Pierre. Transformées de Fourier des fonctions sommables. Proc. Int. Congress Mathematicians 114–131 (1962).Google Scholar
  34. [34]
    Kampen, Egbertus R. van. Almost periodic functions and compact groups. Ann. of Math. 37, 78–91 (1936).MathSciNetzbMATHCrossRefGoogle Scholar
  35. [35]
    Kelvin, Lord (William Thomson), and Peter Guthrie Tait. Treatise on natural philosophy. Cambrige University Press, 1923.Google Scholar
  36. [36]
    Krein, M. G. A principle of duality for a bicompact group and a square-block algebra (In Russian). Dokl. Akad. Nauk SSSR 69, 725–728 (1949).MathSciNetGoogle Scholar
  37. [37]
    Leja, F. Sur les groupes abstraits continus. Annales de la société polonaise de mathématiques III, 153 (1925).zbMATHGoogle Scholar
  38. [38]
    Leja, F. Sur la notion de groupe abstrait topologique. Fund Math. 9, 37–44 (1927).zbMATHGoogle Scholar
  39. [39]
    Leptin, Horst. Sur l'algèbre de Fourier d'un groupe localement compact. C. R. Acad. Sci. Paries, Sér. A 266, 1180–1182 (1968).MathSciNetzbMATHGoogle Scholar
  40. [40]
    Maak, Wilhelm. Fasperiodische Funktionen. Second edition. Springer, Berlin, 1967.zbMATHCrossRefGoogle Scholar
  41. [41]
    Mackey, George W. On induced representations of groups. Amer. J. Math. 73, 576–592 (1951).MathSciNetzbMATHCrossRefGoogle Scholar
  42. [42]
    Mackey, George W. Induced representations of locally compact groups I. Amm. of Math. 55, 101–139 (1952).MathSciNetzbMATHGoogle Scholar
  43. [43]
    Mackey, George W. Induced representations of locally compact groups. Acta Math. 99, 265–311 (1958).MathSciNetCrossRefGoogle Scholar
  44. [44]
    Mackey, George W. Commutative Banach algebras. Notas de matematica 17, Rio de Janiero, 1959.Google Scholar
  45. [45]
    Mackey, George W. Unitary group representations in physics, probability and number theory. Benjamin Cummings Publishing Company, Reading, 1978.zbMATHGoogle Scholar
  46. [46]
    Malliavin, Paul. Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts. Inst. Hautes Etudes Sci. Publ. Math. 2, 61–68 (1959).MathSciNetzbMATHCrossRefGoogle Scholar
  47. [47]
    Montgomery, Deane, and Leo Zippin. Small subgroups of finitedimensional groups. Ann. of Math. 56, 213–241 (1952).MathSciNetzbMATHCrossRefGoogle Scholar
  48. [48]
    Nachbin, Leopoldo. On the finite dimensionality of every irreducible unitary representation of a compact group. Proc. Amer. Math. Soc. 12, 11–12 (1961).MathSciNetzbMATHCrossRefGoogle Scholar
  49. [49]
    Naimark, M. A. Normed rings (In Russian). English translation: Noordhoff, Groningen, 1964.zbMATHGoogle Scholar
  50. [50]
    Neumann, John von. Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren. Math. Ann. 102, 370–427 (1929).MathSciNetzbMATHCrossRefGoogle Scholar
  51. [51]
    Neumann, John von. Ueber die analytischen Eigenschaften von Gruppen linearer Transformationen und ihrer Darstellungen. Math. Z. 30, 3–42 (1929).MathSciNetCrossRefGoogle Scholar
  52. [52]
    Neumann, John von. Zum Haarschen Mass in topologischen Gruppen. Compositio Math. 1, 106–114 (1934).MathSciNetzbMATHGoogle Scholar
  53. [53]
    Neumann, John von. Almost periodic functions in a group I. Trans. Amer. Math. Soc. 36, 445–492 (1934).MathSciNetzbMATHCrossRefGoogle Scholar
  54. [54]
    Peter, F., and Hermann Weyl. Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe. Math. Ann. 97, 737–755 (1927).MathSciNetzbMATHCrossRefGoogle Scholar
  55. [55]
    Pier, Jean-Paul. Amenable locally compact groups. John Wiley, New York, 1984.zbMATHGoogle Scholar
  56. [56]
    Pier, Jean-Paul. Mesures invariantes. De Lebesgue à nos jours. Historia Mathematica 13, 229–240 (1986).MathSciNetzbMATHCrossRefGoogle Scholar
  57. [57]
    Pier, Jean-Paul. L'apparition de la théorie des groupes topologiques. Cahiers du séminaire d'histoire des mathématiques 9, 1–21 (1988).MathSciNetGoogle Scholar
  58. [58]
    Plancherel, Michel. Contribution à l'étude de la représentation d'une fonction arbitraire par les intégrales définies. Rend. Circ. Mat. Palermo 30, 289–335 (1910).zbMATHCrossRefGoogle Scholar
  59. [59]
    Poincaré, Henri. La valeur de la science, 1913. Reprint: Flammarion, Paris, 1948.Google Scholar
  60. [60]
    Pontrjagin, L. S. Sur les groupes abéliens continus. C. R. Acad. Sci. Paris 198, 328–330 (1934).zbMATHGoogle Scholar
  61. [61]
    Pontrjagin, L. S. Sur les groupes topologiques et le cinquième problème de Hilbert. C. R. Acad. Sci. Paris 198, 238–240 (1934).zbMATHGoogle Scholar
  62. [62]
    Pontrjagin, L. S. The theory of topological commutative groups. Ann. of Math. 35, 361–388 (1934).MathSciNetzbMATHCrossRefGoogle Scholar
  63. [63]
    Pontrjagin, L. S. Continuous groups (in Russian). GITTL, Moscow, 1938. English translation: Topological groups. Princeton University Press, Princeton, 1939.Google Scholar
  64. [64]
    Reiter, Hans. On some properties of locally compact groups. Nederl. Wetensch. Proc., Ser. A 68, 697–701 (1965).MathSciNetzbMATHCrossRefGoogle Scholar
  65. [65]
    Rickart, Charles E. Banach algebras with an adjoint operation. Ann. of Math. 47, 528–550 (1946).MathSciNetzbMATHCrossRefGoogle Scholar
  66. [66]
    Riesz, Frédéric. Sur les systèmes orthogonaux de fonctions. C. R. Acad. Sci. Paris 144, 615–619 (1907).zbMATHGoogle Scholar
  67. [67]
    Riesz, Frédéric. Ueber orthogonale Funktionensysteme. Nachr. Akad. Wiss. Göttingen; math.-phys. Kl. 116–122 (1907).Google Scholar
  68. [68]
    Riesz, Frédéric. Les systèmes d'équations linéaires à une infinité d'inconnues. Gauthier-Villars, Paris, 1913.zbMATHGoogle Scholar
  69. [69]
    Schreier, Otto. Abstrakte kontinuierliche Gruppen. Abh. Math. Sem. Univ. Hamburg 4, 15–32 (1925).MathSciNetzbMATHCrossRefGoogle Scholar
  70. [70]
    Schwartz, Laurent. Sur une propriété de synthèse spectrale dans les groupes non compacts. C. R. Acad. sci. Paris 227, 424–426 (1948).MathSciNetzbMATHGoogle Scholar
  71. [71]
    Segal, Irving E. The group ring of a locally compact group I. Proc. Nat. Acad. Sci. U.S.A. 27, 348–352 (1941).MathSciNetzbMATHCrossRefGoogle Scholar
  72. [72]
    Segal, Irving E. The group algebra of a locally compact group. Trans. Amer. Math. Soc. 61, 69–105 (1947).MathSciNetzbMATHCrossRefGoogle Scholar
  73. [73]
    Silov, G. E. On normed rings (In Russian). Trudy Mat. Inst. im. V. A. Steklova. 21. Akad. Nauk SSSR (1947).Google Scholar
  74. [74]
    Tannaka, Tadao. Ueber den Dualitätssatz der nichtkommutativen topologischen Gruppen. Tôhoku Math. J. 45, 1–12 (1939).zbMATHGoogle Scholar
  75. [75]
    Varopoulos, Nicholas Th. Tensor algebras and harmonic analysis. Acta Math. 119, 51–112 (1967).MathSciNetzbMATHCrossRefGoogle Scholar
  76. [76]
    Voss, A. Differential-und Integralrechnung, 1899. Enzyklopädie der Wissenschaften, Vol, II, 54–134. Teubner, Berlin, 1916.Google Scholar
  77. [77]
    Weil, André. Sur les groupes topologiques et les groupes mesurés. C. R. Acad. Sci. Paris 202, 1147–1149 (1936).zbMATHGoogle Scholar
  78. [78]
    Weil, André. L'intégration dans les groupes topologiques et ses applications, 1940. Reprint: Hermann, Paris, 1953.Google Scholar
  79. [79]
    Wendel, James. Left centralizers and isomoprhisms of group algebras. Pacific J. Math. 2, 251–261 (1952).MathSciNetzbMATHCrossRefGoogle Scholar
  80. [80]
    Weyl, Hermann. The classical groups, their invariants and representations. Princeton Un. Press, 1939.Google Scholar
  81. [81]
    Weyl, Hermann. Relativity theory as a stimulus in mathematical research. Gesammelte Abhandlungen, Vol. IV. Springer, Berlin, 1968.Google Scholar
  82. [82]
    Wiener, Norbert. Tauberian theorems. Ann. of Math. 33, 1–100 (1932).MathSciNetzbMATHCrossRefGoogle Scholar
  83. [83]
    Wiener, Norbert. I am a mathematician. MIT Press, Cambridge, Massachusetts, 1956.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Jean-Paul Pier
    • 1
  1. 1.Séminaire de mathématiqueCentre universitaire de LuxembourgLuxembourg

Personalised recommendations