| 1. |
- Englis, M., et al.
(författare)
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Hankel operators and the Dixmier trace on the Hardy space
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 94, s. 337-356
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Tidskriftsartikel (refereegranskat)abstract
- We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there exist Dixmier-class Hankel operators that are not measurable (that is, their Dixmier trace depends on the choice of the underlying Banach limit), as well as Dixmier-class Hankel operators that do not belong to the Schatten-Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed.
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| 2. |
- Englis, M., et al.
(författare)
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Toeplitz Operators on Higher Cauchy-Riemann Spaces
- 2017
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Ingår i: Documenta Mathematica. - 1431-0643 .- 1431-0635. ; 22, s. 1081-1116
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Tidskriftsartikel (refereegranskat)abstract
- We develop a theory of Toeplitz, and to some extent Hankel, operators on the kernels of powers of the boundary d-bar operator, suggested by Boutet de Monvel and Guillemin, and on their analogues, somewhat better from the point of view of complex analysis, defined using instead the covariant Cauchy-Riemann operators of Peetre and the second author. For the former, Dixmier class membership of these Hankel operators is also discussed. Our main tool are the generalized Toeplitz operators (with pseudodifferential symbols), in particular there appears naturally the problem of finding parametrices of matrices of such operators in situations when the principal symbol fails to be elliptic.
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| 3. |
- Fischer, V., et al.
(författare)
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Degenerate principal series representations of SO(p+1, p)
- 2015
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Ingår i: Monatshefte Fur Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 176:1, s. 87-105
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Tidskriftsartikel (refereegranskat)abstract
- For odd, the Lie group has a family of complementary series representations realized on the space of real skew symmetric matrices, similar to the Stein's complementary series for . We consider their restriction on the subgroup and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of , and also irreducible under a maximal parabolic subgroup of G.
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| 4. |
- Kim, I., et al.
(författare)
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Convex real projective structures and Weil's local rigidity theorem
- 2018
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Ingår i: Journal De Mathematiques Pures Et Appliquees. - : Elsevier BV. - 0021-7824. ; 116, s. 40-51
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Tidskriftsartikel (refereegranskat)abstract
- For an n-dimensional real hyperbolic manifold M, we calculate the Zariski tangent space of a character variety chi(pi(1)(M), SL(n +1, R), n > 2 at Fuchsian locus to show that the tangent space consists of cubic forms. Furthermore we prove the Weil's local rigidity theorem for uniform hyperbolic lattices using real projective structures. (C) 2018 Elsevier Masson SAS. All rights reserved.
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| 5. |
- Kim, Inkang, et al.
(författare)
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Eichler–Shimura isomorphism for complex hyperbolic lattices
- 2017
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 121, s. 452-460
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Tidskriftsartikel (refereegranskat)abstract
- © 2017 Elsevier B.V. We consider the cohomology group H 1 (Γ,ρ) of a discrete subgroup Γ⊂G=SU(n,1) and the symmetric tensor representation ρ on S m (C n+1 ). We give an elementary proof of the Eichler–Shimura isomorphism that harmonic forms H 1 (Γ∖G∕K,ρ) are (0,1)-forms for the automorphic holomorphic bundle induced by the representation S m (C n ) of K.
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| 6. |
- Kim, I., et al.
(författare)
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KAHLER METRIC ON THE SPACE OF CONVEX REAL PROJECTIVE STRUCTURES ON SURFACE
- 2017
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Ingår i: Journal of Differential Geometry. - : International Press of Boston. - 0022-040X .- 1945-743X. ; 106:1, s. 127-137
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the space of convex real projective structures on a surface of genus g >= 2 admits a mapping class group invariant Kahler metric where Teichmuller space with Weil-Petersson metric is a totally geodesic complex submanifold.
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| 7. |
- Kim, Inkang, et al.
(författare)
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Local rigidity of complex hyperbolic lattices in semisimple Lie groups
- 2018
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Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - 0305-0041 .- 1469-8064. ; 165:1, s. 179-191
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Tidskriftsartikel (refereegranskat)abstract
- We show the local rigidity of complex hyperbolic lattices in classical Hermitian semisimple Lie groups, SU(p, q), Sp(2n + 2, ), SO∗(2n + 2), SO(2n, 2). This reproves or generalises some results in [2, 9, 11, 15].
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| 8. |
- Mollers, J., et al.
(författare)
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On boundary value problems for some conformally invariant differential operators
- 2016
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Ingår i: Communications in Partial Differential Equations. - : Informa UK Limited. - 0360-5302 .- 1532-4133. ; 41:4, s. 609-643
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Tidskriftsartikel (refereegranskat)abstract
- We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace, respectively, Heisenberg subgroup. These operators are shown to be self-adjoint in certain Sobolev type spaces and the related boundary value problems are proven to have unique solutions in these spaces. We further find the corresponding Poisson transforms explicitly in terms of their integral kernels and show that they are isometric between Sobolev spaces and extend to bounded operators between certain L-p-spaces.The conformal invariance of the differential operators allows us to apply unitary representation theory of reductive Lie groups, in particular recently developed methods for restriction problems.
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| 9. |
- Reza, Md Ramiz, et al.
(författare)
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Hausdorff Moment Sequences Induced by Rational Functions
- 2019
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Ingår i: Complex Analysis and Operator Theory. - : Springer Science and Business Media LLC. - 1661-8262 .- 1661-8254. ; 13:8, s. 4117-4142
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Tidskriftsartikel (refereegranskat)abstract
- We study the Hausdorff moment problem for a class of sequences, namely (r(n))n∈Z+, where r is a rational function in the complex plane. We obtain a necessary condition for such sequence to be a Hausdorff moment sequence. We found an interesting connection between Hausdorff moment problem for this class of sequences with finite divided differences and convolution of complex exponential functions. We provide a sufficient condition on the zeros and poles of a rational function r so that (r(n))n∈Z+ is a Hausdorff moment sequence. G. Misra asked whether the module tensor product of a subnormal module with the Hardy module over the polynomial ring is again a subnormal module or not. Using our necessary condition we answer the question of G. Misra in negative. Finally, we obtain a characterization of all real polynomials p of degree up to 4 and a certain class of real polynomials of degree 5 for which the sequence (1/p(n))n∈Z+ is a Hausdorff moment sequence.
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| 10. |
- Sahi, S., et al.
(författare)
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Positivity of Shimura operators
- 2019
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 26:2, s. 587-626
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we answer some questions of G. Shimura on the positivity of certain invariant differential operators that play a key role in the study of nearly holomorphic automorphic forms in higher rank. Our main result expresses the eigenvalues of Shimura operators in terms of certain polynomials introduced by A. Okounkov, which leads to an explicit answer to Shimura's questions.
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