Systems of singular integral operators on spheres
HTML articles powered by AMS MathViewer
- by Daniel A. Levine
- Trans. Amer. Math. Soc. 144 (1969), 493-522
- DOI: https://doi.org/10.1090/S0002-9947-1969-0412743-1
- PDF | Request permission
References
- H. Boerner, Representations of groups, North-Holland, Amsterdam, 1963.
N. Bourbaki, Éléments de mathématique, Fase. XXVII, Algèbre commutative, Hermann, Paris, 1961.
- 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). MR 0123834
- A.-P. Calderón, Singular integrals, Bull. Amer. Math. Soc. 72 (1966), 427–465. MR 209918, DOI 10.1090/S0002-9904-1966-11492-1
- A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901–921. MR 100768, DOI 10.2307/2372441 R. Godement, “Localites simples. I and II” in Séminaire H. Cartan et C. Chevalley, 8$^{e}$ année, École Norm. Sup., Paris, 1956.
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- S. Helgason, Some results on invariant theory, Bull. Amer. Math. Soc. 68 (1962), 367–371. MR 166303, DOI 10.1090/S0002-9904-1962-10812-X
- Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI 10.1002/cpa.3160180307
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. MR 176362, DOI 10.1002/cpa.3160180121
- Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404. MR 158024, DOI 10.2307/2373130
- Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. MR 0100591 D. A. Levine, Singular integral operators on spheres, Ph.D. Thesis, Princeton University, Princeton, N. J., 1968.
- S. G. Mihlin, Mnogomernye singulyarnye integraly i integral′nye uravneniya, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1962 (Russian). MR 0155165
- B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17–92. MR 199636, DOI 10.1090/S0002-9947-1965-0199636-9 F. D. Murnaghan, The theory of group representations, Johns Hopkins Press, Baltimore, Maryland, 1938. R. S. Palais, “Differential operators on vector bundles” in Seminar on the Atiyah-Singer index theorem, Princeton Univ. Press, Princeton, N. J., 1965.
- Richard S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. MR 0198494, DOI 10.1515/9781400882045
- 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). MR 0072531
- R. T. Seeley, Singular integrals on compact manifolds, Amer. J. Math. 81 (1959), 658–690. MR 110022, DOI 10.2307/2372921
- R. T. Seeley, Spherical harmonics, Amer. Math. Monthly 73 (1966), no. 4, 115–121. MR 201695, DOI 10.2307/2313760 E. M. Stein, Integrales singulières et fonctions differentiables de plusieurs variables, Publications Mathématiques d’Orsay, 1967.
- 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. MR 223492, DOI 10.2307/2373431
- Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158 —, Gruppentheorie und Quantenmechanik, 2nd ed., Hirzel, Leipzig, 1931; English transl., Dover, New York, 1950.
- 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. MR 0120249, DOI 10.1007/978-3-662-29244-0 A. Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge, 1959.
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 144 (1969), 493-522
- MSC: Primary 43A85
- DOI: https://doi.org/10.1090/S0002-9947-1969-0412743-1
- MathSciNet review: 0412743