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- Induced Representations of Locally Compact Groups , pp. 333 - 339Publisher: Cambridge University PressPrint publication year: 2012
References
[1] , A weak containment theorem for groups with a quotient R-group. Trans. Amer. Math. Soc., 128 (1967), 277–90.Google Scholar
[2] , A description of the topology on the dual spaces of certain locally compact groups. Trans. Amer. Math. Soc., 132 (1968), 175–212.Google Scholar
[3] , A separable group having a discrete dual space is compact. J. Funct. Anal., 10 (1972), 131–48.Google Scholar
[5] , On the continuity of Mackey's extension process. J. Funct. Anal., 56 (1984), 233–50.Google Scholar
[6] and , Multiplier representations of abelian groups. J. Funct. Anal., 14 (1973), 299–324.Google Scholar
[7] and , Representations of theMautner group and cocycles of an irrational rotation. Michigan Math. J., 33 (1986), 221–9.Google Scholar
[8] and , C*-algebras associated to two-step nilpotent groups. Contemporary Math., 120 (1991), 1–6.Google Scholar
[9] and , The primitive ideal space of two-step nilpotent group C*-algebras. J. Funct. Anal., 124 (1994), 389–426.Google Scholar
[10] and , Some pathologies in the Mackey analysis for a certain nonseparable group. J. Funct. Anal., 39 (1980), 375–80.Google Scholar
[11] and , The Hausdorff dual problem for connected groups. J. Funct. Anal., 43 (1981), 60–8.Google Scholar
[12] and , Riemann–Lebesgue subsets of ℝn and representations which vanish at infinity. J. Funct. Anal., 28 (1978), 168–81.Google Scholar
[13] and , On asymptotic behaviour of induced representations. Canad. J. Math., 34 (1982), 220–32.Google Scholar
[14] , The role of minimal idempotents in the representation theory of locally compact groups. Proc. Edinb. Math. Soc., 23 (1980), 229–38.Google Scholar
[15] and , Theory of Group Representations and Applications. Warsaw: Polish Scientific Publishers, 1977.
[16] , A characterization of locally compact amenable groups by means of tensor products. Arch. Math. (Basel), 52 (1989), 424–7.Google Scholar
[17] and , On Mackey's irreducibility criterion for induced representations. Int. Math. Res. Not., 38 (2003), 2095–101.Google Scholar
[18] and , Topological Frobenius properties for nilpotent groups. Math. Scand., 63 (1988), 282–96.Google Scholar
[19] and , Wavelets from square-integrable representations. SIAM J. Math. Anal., 27 (1996), 594–608.Google Scholar
[20] , Irreducible induced representations of ICC groups. Math. Ann., 294 (1992), 37–47.Google Scholar
[21] , On induced representations of discrete groups. Proc. Amer. Math. Soc., 118 (1993), 301–9.Google Scholar
[23] , On induced representations. II. Infinitesimal induction. Amer. J. Math., 83 (1961), 499–512.Google Scholar
[25] , A theorem on induced representations. Proc. Amer. Math. Soc., 13 (1962), 881–4.Google Scholar
[27] , Group extension representations and the structure space. Pacific J. Math., 15 (1965), 1101–13.Google Scholar
[28] , Dual topology of a nilpotent Lie group. Ann. Sci. Éc. Norm. Sup. (4), 6 (1973), 407–11.Google Scholar
[30] , and , Integral operators and the compactness of induced representations. Trans. Amer. Math. Soc., 164 (1972), 461–77.Google Scholar
[31] , Induced representations of discrete groups. Proc. Amer. Math. Soc., 47 (1975), 279–87.Google Scholar
[32] and , Intertwining operators for representations induced from uniform subgroups. Acta Math., 136 (1976), 275–301.Google Scholar
[33] and , Representations of Nilpotent Lie Groups and their Applications. Part 1: Basic Theory and Examples. Cambridge: Cambridge University Press, 1990.
[35] , Sur les représentations unitaires des groupes de Lie nilpotents. VI.Canad. J. Math., 12 (1960), 324–52.Google Scholar
[36] , Les Algèbres d'Opérateurs dans l'Espace Hilbertien. Paris: Gauthier-Villars, 1969.
[37] , C*-algebras. Amsterdam: North-Holland, 1977.
[38] , Mackey'sche Theorie irreduzibler Darstellungen und Topologie im Dual lokalkompakter Gruppen. Diplomarbeit, Universität Paderborn, 1986.
[39] , Fundamentals of Infinite Dimensional Representation Theory. Boca Raton, FL: Chapman and Hall/CRC, 2000.
[41] , Erratum to “On Mackey's tensor product theorem”. Duke Math. J., 41 (1974), 691.Google Scholar
[42] , Representations induced from conjugate subgroups. Indiana J. Math., 19 (1977), 167–71.Google Scholar
[43] , An intertwining number theorem for induced representations. Nanta Math., 11 (1978), 164–73.Google Scholar
[44] , Über Integralzerlegungen von Darstellungen nilpotenter Liegruppen. Manuscr. Math., 9 (1979), 279–90.Google Scholar
[45] , and , Topological Frobenius reciprocity for projective limits of Lie groups. Math. Z., 165 (1979), 19–28.Google Scholar
[47] , A new proof that nilpotent groups are CCR. Proc. Amer. Math. Soc., 13 (1962), 93–9.Google Scholar
[48] , A Hausdorff topology on the closed subsets of a locally compact non-Hausdorff space. Proc. Amer. Math. Soc., 13 (1962), 472–6.Google Scholar
[49] , Weak containment and induced representations of groups. Canad. J. Math., 14 (1962), 237–68.Google Scholar
[50] , Weak containment andKronecker products of group representations. Pacific J. Math., 13 (1963), 503–10.Google Scholar
[51] , Weak containment and induced representations of groups. II. Trans. Amer. Math. Soc., 110 (1964), 424–47.Google Scholar
[52] , A new look at Mackey's imprimitivity theorem. In: Conference on Harmonic Analysis, Lecture Notes in Mathematics 266. Berlin: Springer-Verlag 1972, pp. 43–58.
[53] and , Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 1: Basic Representation Theory of Groups and Algebras. Boston: Academic Press, 1988.
[54] and , Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 2: Banach *-Algebraic Bundles, Induced Representations, and the Generalized Mackey Analysis. Boston: Academic Press, 1988.
[55] , A Course in Abstract Harmonic Analysis. Boca Raton: CRC Press, 1995.
[56] , Über Relationen zwischen den Charakteren einer Gruppe und denen ihrer Untergruppen. Sitz. Preuss. Akad.Wiss. (1898), 501–15; also pp. 104–18 in Frobenius's Gesammelte Abhandlungen, Vol. III. Berlin: Springer, 1968.
[57] , Linear Analysis and Representation Theory. GrundlehrenMath.Wiss. 198. Berlin: Springer, 1973.
[58] and , On the embedding of normed rings into the ring of operators in Hilbert space. Mat. Sb. N. S., 12(54) (1943), 197–213.Google Scholar
[59] and , Irreducible unitary representations of locally bicompact groups. Mat. Sb. N. S., 13(55) (1943), 301–16.Google Scholar
[60] , Locally compact transformation groups. Trans. Amer. Math. Soc., 101 (1961), 124–38.Google Scholar
[63] , Les fonctions de type positif et la thèorie des groupes. Trans. Amer. Math. Soc., 63 (1948), 1–84.Google Scholar
[64] , Weak containment and weak Frobenius reciprocity. Proc. Amer. Math. Soc., 54 (1976), 417–22.Google Scholar
[65] , Induced representations and finite volume homogeneous spaces. J. Funct. Anal., 24 (1977), 223–40.Google Scholar
[66] and , The structure of crossed product C*-algebras: a proof of the generalized Effros–Hahn conjecture. Invent. Math., 52 (1979), 283–98.Google Scholar
[67] , Invariant Means on Topological Groups. NewYork: van Nostrand, 1969.
[68] , Amenable actions of locally compact groups. J. Funct. Anal., 4 (1969), 295–315.Google Scholar
[69] , and , Compact open sets in duals and projections in L1-algebras of certain semi-direct product groups. Math. Proc. Cambridge Phil. Soc., 111 (1992), 545–56.Google Scholar
[70] and , Compactness conditions in topological groups. J. Reine Angew. Math., 246 (1971), 1–40.Google Scholar
[72] , Weak Frobenius reciprocity and compactness conditions in topological groups. Pacific J. Math., 82 (1979), 387–406.Google Scholar
[73] and , Abstract Harmonic Analysis. I. Berlin: Springer, 1963.
[74] and , Abstract Harmonic Analysis. II. Berlin: Springer, 1970.
[75] , On representations of discrete, finitely generated, torsion-free, nilpotent groups. Pacific J. Math., 73 (1977), 281–305.Google Scholar
[76] , The Fourier transform for nilpotent locally compact groups. Pacific J. Math., 73 (1977), 307–27.Google Scholar
[77] and , Asymptotic properties of unitary representations. J. Funct. Anal., 32 (1979), 72–96.Google Scholar
[78] , Groups whose regular representation weakly contains all unitary representations. Studia Math., 24 (1964), 37–59.Google Scholar
[79] and , Fundamentals of the Theory of Operator Algebras. I. New York: Academic Press, 1983.
[80] and , Fundamentals of the Theory of Operator Algebras. II. New York: Academic Press, 1986.
[81] , Primitive ideal spaces of groups with relatively compact conjugacy classes. Arch. Math. (Basel), 32 (1979), 16–24.Google Scholar
[83] , Weak containment and tensor products of group representations. II. Math. Ann., 270 (1985), 1–15.Google Scholar
[84] , On topological Frobenius reciprocity for locally compact groups. Arch. Math. (Basel), 48 (1987), 286–97.Google Scholar
[85] , Topological Frobenius properties for nilpotent groups. II. Math. Scand., 68 (1991), 89–107.Google Scholar
[86] , A Course in Commutative Banach Algebras. Graduate Texts in Mathematics 246. New York: Springer, 2009.
[87] and , The Glimm ideal space of a two-step nilpotent locally compact group. Proc. Edinb. Math. Soc., 44 (2001), 505–26.Google Scholar
[88] and , Minimal projections in L1-algebras and open points in the dual spaces of semi-direct product groups. J. London Math. Soc., 53 (1996), 141–57.Google Scholar
[90] , The structure of some induced representations. Duke Math. J., 29 (1962), 555–72.Google Scholar
[92] , Representations induced from compact subgroups. Amer. J. Math., 88 (1966), 544–52.Google Scholar
[93] , Representation Theory of Semisimple Groups: An Overview Based on Examples. Princeton, NJ: Princeton University Press, 1986.
[94] , On the Frobenius reciprocity theorem for square-integrable representations. Pacific J. Math., 53 (1974), 465–71.Google Scholar
[95] and , Resolution of the wavefront set using continuous shearlets. Trans. Amer. Math. Soc., 361 (2009), 2719–54.Google Scholar
[96] , Group Representations. Lecture Notes in Mathematics 388. Berlin: Springer, 1974.
[97] and , The primitive dual space of [FC]− -groups. J. Funct. Anal., 15 (1974), 279–96.Google Scholar
[98] , Positive definite functions and induced representations. Duke Math. J., 27 (1960), 569–79.Google Scholar
[99] , Imprimitivity for representations of locally compact groups. I.Proc. Nat. Acad. Sci. USA, 35 (1949), 537–45.Google Scholar
[101] , Induced representations of locally compact groups. I. Ann. of Math., 55 (1952), 101–39.Google Scholar
[102] , Induced representations of locally compact groups. II: The Frobenius theorem. Ann. of Math., 58 (1953), 193–220.Google Scholar
[103] , Unitary representations of group extensions. I. Acta Math., 99 (1958), 265–311.Google Scholar
[104] , Induced Representations of Groups and Quantum Mechanics. New York: Benjamin, 1968.
[105] , The Theory of Unitary Group Representations. Chicago: The University of Chicago Press, 1976.
[106] , Unitary Group Representations in Physics, Probability, and Number Theory. Mathematics Lecture Note Series 55. Reading, MA: Benjamin/Cummings, 1978.
[107] , Unitary representations of locally compact groups. II. Ann. of Math., 52 (1950), 528–56.Google Scholar
[108] , A generalization of the Frobenius reciprocity theorem. Proc. Nat. Acad. Sci. USA, 37 (1951), 431–5.Google Scholar
[110] , On the Frobenius reciprocity theorem for locally compact groups. Pacific J. Math., 12 (1962), 359–65.Google Scholar
[111] , Groups with finite dimensional irreducible representations. Trans. Amer. Math. Soc., 166 (1972), 401–10.Google Scholar
[112] and , A reciprocity theorem for tensor products of group representations. Proc. Amer. Math. Soc., 64 (1977), 361–4.Google Scholar
[113] and , Square integrable representations of nilpotent Lie groups. Trans. Amer. Math. Soc., 185 (1973), 445–62.Google Scholar
[114] , Topological Frobenius properties for nilpotent Lie groups. Rev. Roumaine Math. Pures Appl., 19 (1974), 421–5.Google Scholar
[115] , The failure of the topological Frobenius property for nilpotent Lie groups. Math. Scand., 45 (1979), 305–10.Google Scholar
[116] , The failure of the topological Frobenius property for nilpotent Lie groups. II. Math. Ann., 256 (1981), 561–8.Google Scholar
[117] , Unitary Representations and Coadjoint Orbits of Low-dimensional Nilpotent Lie Groups. Queen's Papers in Pure and Applied Mathematics 63. Kingston, Ont., 1983.
[118] , The Stone–Č. ech compactification of Prim A. Bull. Austral. Math. Soc., 52 (1995), 377–83.Google Scholar
[119] , Some remarks on induced representations of infinite discrete groups. Math. Ann., 284 (1989), 91–102.Google Scholar
[120] , Induced representations and a newproof of the imprimitivity theorem.J. Funct. Anal., 31 (1979), 355–9.Google Scholar
[121] and , On the structure of twisted group C*-algebras. Trans. Amer. Math. Soc., 334 (1992), 685–718.Google Scholar
[122] , Analysis Now. Graduate Texts in Mathematics 118. New York: Springer-Verlag, 1989.
[123] , Der Raum der primitiven Ideale von endlichen Erweiterungen lokalkompakter Gruppen. Arch. Math. (Basel), 28 (1977), 133–8.Google Scholar
[124] , Simple quotients of group C*-algebras for two step nilpotent groups and connected Lie groups. Ann. Éc. Norm. Sup. (4), 16 (1983), 151–72.Google Scholar
[125] , Topological Groups. Princeton Mathematical Series 2. Princeton, NJ: Princeton University Press, 1939. Translated from the Russian by .
[126] , On C∞-vectors and intertwining bilinear forms for representations of Lie groups. J. Funct. Anal., 9 (1972), 87–120.Google Scholar
[127] , On the irreducibility of an induced representation. Pacific J. Math., 93 (1981), 163–79.Google Scholar
[128] , On the irreducibility of an induced representation. II. Proc. Amer. Math. Soc., 86 (1982), 345–8.Google Scholar
[129] , On group C*-algebras of bounded representation dimension. Trans. Amer. Math. Soc., 272 (1982), 629–44.Google Scholar
[130] , Discrete Subgroups of Lie Groups. New York: Springer, 1972.
[131] , Non-transitive quasi-orbits in Mackey's analysis of group extensions. Acta Math., 137 (1976), 17–48.Google Scholar
[132] , Unitary representations induced from compact subgroups. Studia Math., 42 (1972), 145–75.Google Scholar
[134] , Unitary representations of group extensions: an algebraic approach to the theory of Mackey and Blattner. Studies in Analysis, Adv. Math. Suppl. Studies (1969), 43–82.
[135] , Introduction to the Representation Theory of Compact and Locally Compact Groups. LMS Lecture Note Series 80. Cambridge: Cambridge University Press, 1983.
[136] , Finiteness Conditions and Generalized Soluble Groups. I. Berlin: Springer, 1972.
[137] , The C*-algebras of some real and p-adic solvable groups. Pacific J. Math., 65 (1976), 175–92.Google Scholar
[138] , Fourier Analysis on Groups. Interscience Tracts in Pure and Applied Mathematics 12. New York: Interscience, 1960.
[139] , Topology and the duals of certain locally compact groups. Trans. Amer. Math. Soc., 150 (1970), 477–89.Google Scholar
[140] , Compact and Hilbert–Schmidt induced representations. Duke Math. J., 41 (1974), 89–102.Google Scholar
[142] and , Extensions of the Heisenberg group and wavelet analysis in the plane. In: Spline Functions and the Theory of Wavelets, CRM Proceedings and Lecture Notes 18, eds., and (1999), 99–107.
[143] , Irreducible representations of operator algebras. Bull. Amer. Math. Soc., 53 (1947), 73–88.Google Scholar
[144] , On the decomposition of a commutative normed ring into a direct sum of ideals. Mat. Sb., 32 (1954), 353–64.Google Scholar
[145] , Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton, NJ: Princeton University Press, 1993.
[146] and , Introduction to Fourier Analysis on Euclidean Spaces. Princeton, NJ: Princeton University Press, 1971.
[147] , The connection between the topologies of a locally bicompact group and its dual space. Funkc. Anal. Pril., 5 (1971), 56–63.Google Scholar
[148] , Theory of Operator Algebras. I. Berlin: Springer, 1979.
[149] , Minimal projections, integrable representations and property (T). Arch. Math. (Basel), 43 (1984), 397–406.Google Scholar
[150] , L'intégration dans les Groupes Topologiques et ses Applications. Actualités Sci. et Ind. 869. Paris: Herman et Cie., 1941.
[151] , The topology on the primitive ideal space of transformation group C*-algebras and CCR transformation group C*-algebras. Trans. Amer. Math. Soc., 266 (1981), 335–59.Google Scholar
[152] , The structure of crossed products by smooth actions. J. Austral. Math. Soc., 47 (1989), 226–35.Google Scholar
[153] , Crossed Product C*-algebras. Math. Surveys and Monographs 134. Providence, RI: American Mathematical Society, 2007.
[154] , Trigonometric Series, II. Cambridge: Cambridge University Press, 1959.