| 1. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Dual Space and Hyperdimension of Compact Hypergroups
- 2017
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Ingår i: Glasgow Mathematical Journal. - 0017-0895 .- 1469-509X. ; 59:2, s. 421-435
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Tidskriftsartikel (refereegranskat)abstract
- We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.
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| 2. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Dual space and hyperdimension of compact hypergroups
- 2017
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Ingår i: Glasgow Mathematical Journal. - : Cambridge University Press (CUP). - 0017-0895 .- 1469-509X. ; 59:2, s. 421-435
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Tidskriftsartikel (refereegranskat)abstract
- We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.
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| 3. |
- Blahota, I., et al.
(författare)
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Two-sided Estimates of the Lebesgue Constants with respect to Vilenkin Systems and Applications
- 2018
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Ingår i: Glasgow Mathematical Journal. - : Cambridge University Press. - 0017-0895 .- 1469-509X. ; 60:1, s. 17-34
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.
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| 4. |
- Costa, Antonio F., et al.
(författare)
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ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4
- 2010
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Ingår i: Glasgow Mathematical Journal. - : Cambridge University Press. - 0017-0895 .- 1469-509X. ; 52, s. 401-408
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Tidskriftsartikel (refereegranskat)abstract
- Let g be an integer ≥ 3 and let θg = {X ∈ Mg|Aut(X) ≠ 1d}, where Mg denotes the moduli space of a compact Riemann surface. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belongs to the same connected component. We also prove the connectedness of θg for g = 5, 6, 7 and 8 with the exception of the isolated points given by Kulkarni.
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| 5. |
- Fan, Ming, 1956-
(författare)
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K-envelopes for real interpolation methods
- 2013
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Ingår i: Glasgow Mathematical Journal. - 0017-0895 .- 1469-509X. ; 55:2, s. 293-307
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces(North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the K Φ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.
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| 6. |
- Josefson, Bengt
(författare)
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A Gelfand-Phillips space not containing l(1) whose dual ball is not weak* sequentially compact
- 2001
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Ingår i: Glasgow Mathematical Journal. - 0017-0895 .- 1469-509X. ; 43, s. 125-128
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Tidskriftsartikel (refereegranskat)abstract
- A set D in a Banach space E is called limited if pointwise convergent sequences of linear functionals converge uniformly on D and E is called a GP-space (after Gelfand and Phillips) if every limited set in E is relatively compact. Banach spaces with weak* sequentially compact dual balls (W*SCDB for short) are GP-spaces and l(1)(A) is a GP-space without W*SCDB. Disproving a conjecture of Rosenthal and inspired by James tree space, Hagler and Odell constructed a class of Banach spaces ([HO]-spaces) without both W*SCDB and subspaces isomorphic to l(1). Schlumprecht has shown that there is a subclass of the [HO]-spaces which are also GP-spaces. It is not clear however if any [HO]-construction yields a GP-space-in fact it is not even clear that W*SCDB double left right arrow GP-space is false in general for the class of Banach spaces containing no subspace isomorphic to l(1). In this note the example of Hagler and Odell is modified to yield a GP-space without W*SCDB and without an isomorphic copy of l(1).
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| 7. |
- Kåhrström, Johan
(författare)
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Kostant's problem and parabolic subgroups
- 2010
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Ingår i: Glasgow Mathematical Journal. - 0017-0895 .- 1469-509X. ; 52, s. 19-32
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Tidskriftsartikel (refereegranskat)abstract
- Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I subset of S let g(I) be the corresponding semi-simple subalgebra of g. Denote by W-I the Weyl group of g(I) and let w(o) and w(o)(I) be the longest elements of W and W-I, respectively In this paper we show that the answer to Kostant's problem, i.e. whether the Universal enveloping algebra subjects onto the space of all ad-finite linear transformations of a given module, is the same for the simple highest weight g(I)-module L-I(x) of highest weight x . 0, x is an element of W-I, as the answer for the simple highest weight g-module L(xw(o)(l)w(o)) of highest weight xw(o)(I)w(o). 0. We also give a new description Of the unique quasi-simple quotient of the Verma module Delta(e) with the same annihilator as L(y), y is an element of W.
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| 8. |
- Nystedt, Patrik, 1971-, et al.
(författare)
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EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY
- 2020
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Ingår i: Glasgow Mathematical Journal. - : CAMBRIDGE UNIV PRESS. - 0017-0895 .- 1469-509X. ; 62:1, s. 233-259
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.
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| 9. |
- Schiebold, Cornelia
(författare)
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Explicit solution formulas for the matrix-KP
- 2009
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Ingår i: Glasgow Mathematical Journal. - 0017-0895 .- 1469-509X. ; 51A, s. 147-155
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Tidskriftsartikel (refereegranskat)abstract
- We study a non-commutative version of the Kadomtsev-Petviashvili equations and construct a family of solutions generalizing naturally the soliton to the non-commutative setting. From this we derive explicit solution formulas as well for the scalar as for the matrix-Kadomtsev-Petviashvili equation which still depend on operator parameters.
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| 10. |
- Schiebold, Cornelia
(författare)
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From the non-abelian to the scalar two-dimensional Toda lattice
- 2005
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Ingår i: Glasgow Mathematical Journal. - 0017-0895 .- 1469-509X. ; 47:A, s. 177-189
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Tidskriftsartikel (refereegranskat)abstract
- We extend a solution method used for the one-dimensional Toda lattice in [1], [2] to the two-dimensional Toda lattice. The idea is1. to study the lattice not with values in ℂ but in the Banach algebra ? of bounded operators and2. to derive solutions of the original lattice ℂ-solutions) by applying a functional τ to the ?-solutions constructed in 1.The main advantage of this process is that the derived solution still contains an element of ? as parameter that may be chosen arbitrarily. Therefore, plugging in different types of operators, we can systematically construct a huge variety of solutions. In the second part we focus on applications. We start by rederiving line-solitons and briefly discuss discrete resonance phenomena. Moreover, we are able to find conditions under which it is possible to superpose even countably many line-solitons.
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