| 1. |
- Hedenmalm, Håkan, 1961-
(författare)
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A Beurling-Rudin theorem for H^\infty
- 1987
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Ingår i: Illinois Journal of Mathematics. - 0019-2082 .- 1945-6581. ; 31, s. 629-644
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Tidskriftsartikel (refereegranskat)
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| 2. |
- Jonsson, Jakob, et al.
(författare)
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A spherical initial ideal for Pfaffians
- 2007
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Ingår i: Illinois Journal of Mathematics. - : Duke University Press. - 0019-2082 .- 1945-6581. ; 51:4, s. 1397-1407
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Tidskriftsartikel (refereegranskat)abstract
- We determine a term order on the monomials in the variables X-ij, 1 <= i <= j <= n, such that corresponding initial ideal of the ideal of Pfaffians of degree r of a generic n by n skew-symmetric matrix is the Stanley-Reisner ideal of a join of a simplicial sphere and a simplex. Moreover, we demonstrate that the Pfaffians of the 2r by 2r skew-symmetric submatrices form a, Grobner basis for the given term order. The same methods and similar term orders as for the Pfaffians also yield squarefree initial ideals for certain determinantal ideals. Yet, in contrast to the case of Pfaffians, the corresponding simplicial complexes are balls that do not decompose into a join as above.
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| 3. |
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| 4. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Amenability properties of the central fourier algebra of a compact group
- 2016
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Ingår i: Illinois Journal of Mathematics. - : Duke University Press. - 0019-2082. ; 60:2, s. 505-527
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Tidskriftsartikel (refereegranskat)abstract
- We let the central Fourier algebra, ZA(G), be the subalgebra of functions u in the Fourier algebra A(G) of a compact group, for which u(xyx-1) = u(y) for all x, y in G. We show that this algebra admits bounded point derivations whenever G contains a non-Abelian closed connected subgroup. Conversely when G is virtually Abelian, then ZA(G) is amenable. Furthermore, for virtually Abelian G, we establish which closed ideals admit bounded approximate identities. We also show that ZA(G) is weakly amenable, in fact hyper-Tauberian, exactly when G admits no non-Abelian connected subgroup. We also study the amenability constant of ZA(G) for finite G and exhibit totally disconnected groups G for which ZA(G) is non-amenable. In passing, we establish some properties related to spectral synthesis of subsets of the spectrum of ZA(G).
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| 5. |
- Berndtsson, Bo, 1950
(författare)
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L-2-Extension of partial derivative-closed form
- 2012
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Ingår i: Illinois Journal of Mathematics. - 0019-2082. ; 56:1, s. 21-31
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Tidskriftsartikel (refereegranskat)abstract
- Generalizing and strengthening a recent result of Koziarz, we prove a version of the Ohsawa-Takegoshi-Manivel theorem for partial derivative-closed forms.
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| 6. |
- Björn, Jana
(författare)
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Boundary continuity for quasiminimizers on metric spaces
- 2002
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Ingår i: Illinois Journal of Mathematics. - 0019-2082. ; 46:2, s. 383-403
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Tidskriftsartikel (refereegranskat)abstract
- A pointwise estimate near a boundary point is obtained for quasiminimizers of the energy integral on a doubling metric measure space admitting a Poincare inequality. Wiener type conditions sufficient for the (Holder) continuity of quasiminimizers at a boundary point are also given.
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| 7. |
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| 8. |
- Wikström, Frank
(författare)
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An extremal function for the multiplier algebra of the universal Pick space
- 2004
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Ingår i: Illinois Journal of Mathematics. - 0019-2082. ; 48:3, s. 1053-1065
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Tidskriftsartikel (refereegranskat)abstract
- Let $H^2_m$ be the Hilbert function space on the unit ball in $C{m}$ defined by the kernel $k(z,w) = (1-langle z,w rangle)^{-1}$. For any weak zero set of the multiplier algebra of $H^2_m$, we study a natural extremal function, $E$. We investigate the properties of $E$ and show for example that $E$ tends to $0$ at almost every boundary point. We also give several explicit examples of the extremal function and compare the behaviour of $E$ to the behaviour of $delta^*$ and $g$, the corresponding extremal function for $H^infty$ and the pluricomplex Green function, respectively.
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