Abstract
This paper surveys the existing literature on homogeneous operators and their relationships with projective representations ofPS L(2, ℝ) and other Lie groups. It also includes a list of open problems in this area.
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References
Aleman A, Richter S and Sundberg C, Beurling’s theorem for the Bergman space,Acta Math. 177 (1996) 275–310
Arazy J, A survey of invariant Hilbert spaces of analytic functions on bounded symmetric domains,Contemp. Math. 185 (1995) 7–65
Arveson W, Hadwin D W, Hoover T B and Kymala E E, Circular operators,Indiana U. Math. J. 33 (1984) 583–595
Bagchi B and Misra G, Homogeneous operators and systems of imprimitivity,Contemp. Math. 185 (1995) 67–76
Bagchi B and Misra G, Homogeneous tuples of multiplication operators on twisted Bergman spaces,J. Funct. Anal. 136 (1996) 171–213
Bagchi B and Misra G, Constant characteristic functions and homogeneous operators,J. Op. Theory 37 (1997) 51–65
Bagchi B and Misra G, Scalar perturbations of the Nagy-Foias characteristic function, in: Operator Theory: Advances and Applications, special volume dedicated to the memory of Bela Sz-Nagy (2001) (to appear)
Bagchi B and Misra G, A note on the multipliers and projective representations of semi-simple Lie groups, Special Issue on Ergodic Theory and Harmonic Analysis,Sankhya A62 (2000) 425–432
Bagchi B and Misra G, The homogeneous shifts, preprint
Bagchi B and Misra G, A product formula for homogeneous characteristic functions, preprint
Clark D N and Misra G, On some homogeneous contractions and unitary representations ofSU (1,1),J. Op. Theory 30 (1993) 109–122
Curto R E and Salinas N, Generalized Bergman kernels and the Cowen-Douglas theory,Am. J. Math. 106 (1984) 447–488
Davidson K and Paulsen V I, Polynomially bounded operators,J. Reine Angew. Math. 487 (1997) 153–170
Douglas R G and Misra G, Geometric invariants for resolutions of Hilbert modules, Operator Theory:Advances and Applications 104 (1998) 83–112
Douglas R G, Misra G and Varughese C, On quotient modules — the case of arbitrary multiplicity,J. Funct. Anal. 174 (2000) 364–398
Faraut J and Koranyi A, Analysis on symmetric cones (New York: Oxford Mathematical Monographs, Oxford University Press) (1994)
Geller R, Circularly symmetric normal and subnormal operators,J. d’analyse Math. 32 (1977) 93–117
Hedenmalm H, A factorization theorem for square area-integrable analytic functions,J. Reine Angew. Math. 422 (1991) 45–68
Kerchy L, On Homogeneous Contractions,J. Op. Theory 41 (1999) 121–126
Mackey G W, The theory of unitary group representations (Chicago University Press) (1976)
Misra G, Curvature and the backward shift operators,Proc. Amer. Math. Soc. 91 (1984) 105–107
Misra G, Curvature and discrete series representation ofSL 2(ℝ),J. Int. Eqns Op. Theory 9 (1986) 452–459
Misra G and Sastry N S N, Homogeneous tuples of operators and holomorphic discrete series representation of some classical groups,J. Op. Theory 24 (1990) 23–32
Moore C C, Extensions and low dimensional cohomology theory of locally compact groups, I,Trans. Am. Math. Soc. 113 (1964) 40–63
Sz-Nagy B and Foias C, Harmonic Analysis of Operators on Hilbert Spaces (North Holland) (1970)
Parthasarathy K R, Multipliers on locally compact groups,Lecture Notes in Math. (New York: Springer Verlag) (1969) vol. 93
Paulsen V I, Representations of function algebras, abstract operator spaces and Banach space geometry,J. Funct. Anal. 109 (1992) 113–129
Pisier G, A polynomially bounded operator on Hilbert space which is not similar to a contraction,J. Am. Math. Soc. 10 (1997) 351–369
Sally P J, Analytic continuation of the irreducible unitary representations of the universal covering group of SL(2, ℝ),Mem. Am. Math. Soc. (Providence) (1967) vol. 69
Shields A L, On Möbius bounded operators,Ada Sci. Math. 40 (1978) 371–374
Szegö G, Orthogonal polynomials,Amer. Math. Soc. (Colloquium Publication) (1985) vol. 23
Varadarajan V S, Geometry of quantum theory (New York: Springer Verlag) 1985
Wilkins D R, Operators, Fuchsian groups and automorphic bundles,Math. Ann. 290 (1991) 405–424
Wilkins D R, Homogeneous vector bundles and Cowen-Douglas operators,Int. J. Math. 4 (1993) 503–520
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Bagchi, B., Misra, G. Homogeneous operators and projective representations of the Möbius group: A survey. Proc. Indian Acad. Sci. (Math. Sci.) 111, 415–437 (2001). https://doi.org/10.1007/BF02829616
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DOI: https://doi.org/10.1007/BF02829616