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Systems of singular integral operators on spheres. (English) Zbl 0196.15803


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[1] H. Boerner, Representations of groups, North-Holland, Amsterdam, 1963. · Zbl 0112.26301
[2] N. Bourbaki, Éléments de mathématique, Fase. XXVII, Algèbre commutative, Hermann, Paris, 1961. · Zbl 0108.04002
[3] Alberto-P. Calderón, Integrales singulares y sus aplicaciones a ecuaciones diferenciales hiperbolicas, Cursos y Seminarios de Matemática, Fasc. 3. Universidad de Buenos Aires, Buenos Aires, 1960 (Spanish). · Zbl 0096.06702
[4] A.-P. Calderón, Singular integrals, Bull. Amer. Math. Soc. 72 (1966), 427 – 465. · Zbl 0151.16902
[5] A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901 – 921. · Zbl 0081.33502
[6] R. Godement, “Localites simples. I and II” in Séminaire H. Cartan et C. Chevalley, 8\( ^{e}\) année, École Norm. Sup., Paris, 1956.
[7] SigurÄ’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[8] S. Helgason, Some results on invariant theory, Bull. Amer. Math. Soc. 68 (1962), 367 – 371. · Zbl 0106.25101
[9] Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501 – 517. · Zbl 0125.33401
[10] Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. · Zbl 0121.27504
[11] J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269 – 305. · Zbl 0171.35101
[12] Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327 – 404. · Zbl 0124.26802
[13] Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. · Zbl 0095.15301
[14] D. A. Levine, Singular integral operators on spheres, Ph.D. Thesis, Princeton University, Princeton, N. J., 1968.
[15] Многомерные сингулярные интегралы и интеграл\(^{\приме}\)ные уравнения, Государств. Издат. Физ.-Мат. Лит., Мосцощ, 1962 (Руссиан).
[16] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17 – 92. · Zbl 0139.29002
[17] F. D. Murnaghan, The theory of group representations, Johns Hopkins Press, Baltimore, Maryland, 1938. · Zbl 0022.11807
[18] R. S. Palais, “Differential operators on vector bundles” in Seminar on the Atiyah-Singer index theorem, Princeton Univ. Press, Princeton, N. J., 1965. · Zbl 0137.17002
[19] Richard S. Palais, Seminar on the Atiyah-Singer index theorem, With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. · Zbl 0137.17002
[20] P. Samuel, Méthodes d’algèbre abstraite en géométrie algébrique, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 4, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (French). · Zbl 0146.16901
[21] R. T. Seeley, Singular integrals on compact manifolds, Amer. J. Math. 81 (1959), 658 – 690. · Zbl 0109.33001
[22] R. T. Seeley, Spherical harmonics, Amer. Math. Monthly 73 (1966), no. 4, 115 – 121. · Zbl 0142.03503
[23] E. M. Stein, Integrales singulières et fonctions differentiables de plusieurs variables, Publications Mathématiques d’Orsay, 1967.
[24] E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163 – 196. · Zbl 0157.18303
[25] Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. · Zbl 1024.20501
[26] -, Gruppentheorie und Quantenmechanik, 2nd ed., Hirzel, Leipzig, 1931; English transl., Dover, New York, 1950.
[27] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. · Zbl 0322.13001
[28] A. Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge, 1959. · Zbl 0085.05601
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