https://www.mscand.dk/issue/feed MATHEMATICA SCANDINAVICA 2019-09-21T02:59:12+02:00 Andrew Swann mscand@math.au.dk Open Journal Systems https://www.mscand.dk/article/view/112190 Quasi-symmetry without ratios 2019-09-21T02:59:07+02:00 Jaroslaw Kwapisz mscand@math.au.dk <p>We characterize quasi-symmetric maps between compact metric spaces as <em>homeomorphisms uniformly at all scales</em>.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/114715 The $2$-Hessian and sextactic points on plane algebraic curves 2019-09-21T02:58:54+02:00 Paul Aleksander Maugesten mscand@math.au.dk Torgunn Karoline Moe mscand@math.au.dk <p>In an article from 1865, Arthur Cayley claims that given a plane algebraic curve there exists an associated $2$-Hessian curve that intersects it in its sextactic points. In this paper we fix an error in Cayley's calculations and provide the correct defining polynomial for the $2$-Hessian. In addition, we present a formula for the number of sextactic points on cuspidal curves and tie this formula to the $2$-Hessian. Lastly, we consider the special case of rational curves, where the sextactic points appear as zeros of the Wronski determinant of the 2nd Veronese embedding of the curve.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/113032 A comparison formula for residue currents 2019-09-21T02:58:58+02:00 Richard Lärkäng mscand@math.au.dk <p>Given two ideals $\mathcal {I}$ and $\mathcal {J}$ of holomorphic functions such that $\mathcal {I} \subseteq \mathcal {J}$, we describe a comparison formula relating the Andersson-Wulcan currents of $\mathcal {I}$ and $\mathcal {J}$. More generally, this comparison formula holds for residue currents associated to two generically exact Hermitian complexes together with a morphism between the complexes.</p> <p>One application of the comparison formula is a generalization of the transformation law for Coleff-Herrera products to Andersson-Wulcan currents of Cohen-Macaulay ideals. We also use it to give an analytic proof by means of residue currents of theorems of Hickel, Vasconcelos and Wiebe related to the Jacobian ideal of a holomorphic mapping.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/112071 Uniqueness of norm-preserving extensions of functionals on the space of compact operators 2019-09-21T02:59:12+02:00 Julia Martsinkevitš mscand@math.au.dk Märt Põldvere mscand@math.au.dk <p>Godefroy, Kalton, and Saphar called a closed subspace $Y$ of a Banach space $Z$ an ideal if its annihilator $Y^\bot$ is the kernel of a norm-one projection $P$ on the dual space $Z^\ast$. If $Y$ is an ideal in $Z$ with respect to a projection on $Z^\ast$ whose range is norming for $Z$, then $Y$ is said to be a strict ideal. We study uniqueness of norm-preserving extensions of functionals on the space $\mathcal{K}(X,Y)$ of compact operators between Banach spaces $X$ and $Y$ to the larger space $\mathcal{K}(X,Z)$ under the assumption that $Y$ is a strict ideal in&nbsp;$Z$. Our main results are: (1) if $y^\ast$ is an extreme point of $B_{Y^{\ast} }$ having a unique norm-preserving extension to&nbsp;$Z$, and $x^{\ast\ast} \in B_{X^{\ast\ast} }$, then the only norm-preserving extension of the functional $x^{\ast\ast} \otimes y^\ast \in \mathcal {K}(X,Y)^\ast$ to $\mathcal {K}(X,Z)$ is $x^{\ast\ast} \otimes z^\ast$ where $z^\ast \in Z^\ast$ is the only norm-preserving extension of $y^\ast$ to $Z$; (2) if $\mathcal{K}(X,Y)$ is an ideal in $\mathcal{K}(X,Z)$ and $Y$ has Phelps' property&nbsp;$U$ in its bidual $Y^{\ast\ast}$ (i.e., every bounded linear functional on $Y$ admits a unique norm-preserving extension to $Y^{\ast\ast}$), then $\mathcal{K}(X,Y)$ has property&nbsp;$U$ in $\mathcal{K}(X,Z)$ whenever $X^{\ast\ast}$ has the Radon-Nikodým property.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/112630 A bicategorical interpretation for relative Cuntz-Pimsner algebras 2019-09-21T02:59:03+02:00 Ralf Meyer mscand@math.au.dk Camila F. Sehnem mscand@math.au.dk <p>We interpret the construction of relative Cuntz-Pimsner algebras of correspondences in terms of the correspondence bicategory, as a reflector into a certain sub-bicategory. This generalises a previous characterisation of absolute Cuntz-Pimsner algebras of proper correspondences as colimits in the correspondence bicategory.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/114722 Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$ 2019-09-21T02:58:49+02:00 Corina Ciobotaru mscand@math.au.dk <p>We prove that all parabolically induced unitary representations of the Burger-Mozes universal group $U(F)^{+}$, with $F$ being primitive, are $C_0$. This generalizes the same well-known result for the universal group $U(F)^{+}$, when $F$ is $2$-transitive.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/114725 Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity 2019-09-21T02:58:45+02:00 Shuichi Sato mscand@math.au.dk <p>We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by considering fractional integrals of mixed homogeneity in place of the Riesz potentials of Euclidean structure.</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/115626 Issue covers 2019-08-29T12:56:19+02:00 Mathematica Scandinavica mscand@math.au.dk <p>Issue covers</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/115627 Volume front pages 2019-08-29T12:56:19+02:00 Mathematica Scandinavica mscand@math.au.dk <p>Volume front pages</p> 2019-08-29T00:00:00+02:00 ##submission.copyrightStatement##