International Journal of Mathematics

We study concepts of stability associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the associated dual span bundle and linear stability. Our results imply that stability of the dual span holds under a hypothesis related to the Clifford index of the curve. Furthermore, in some of the cases, we prove that a stronger stability holds: cohomological stability. Finally, using our results we obtain stable vector bundles of slope 3, and prove that they admit theta-divisors.

We investigate KMS states of Fowler's Nica–Toeplitz algebra associated to a compactly aligned product system X over a semigroup P of Hilbert bimodules. This analysis relies on restrictions of these states to the core algebra which satisfy appropriate scaling conditions. The concept of product system of finite type is introduced. If (G, P) is a lattice ordered group and X is a product system of finite type over P satisfying certain coherence properties, we construct KMS_β states of associated to a scalar dynamics from traces on the coefficient algebra of the product system. Our results were motivated by, and generalize some of the results of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers.

We show that in ℂ² if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubharmonic upper envelopes of functions continuous up to the boundary are continuous on the closure of the domain. Using this result we prove that smooth bounded pseudoconvex Reinhardt domains in ℂ² are c-regular.

Given a holomorphic line bundle L on a compact complex torus A, there are two naturally associated holomorphic Ω_A-torsors over A: one is constructed from the Atiyah exact sequence for L, and the other is constructed using the line bundle , where α is the addition map on A × A, and p₁ is the projection of A × A to the first factor. In [I. Biswas, J. Hurtvbise and A. K. Raina, Rank one connections on abelian varieties, Internat. J. Math.22 (2011) 1529–1543], it was shown that these two torsors are isomorphic. The aim here is to produce a canonical isomorphism between them through an explicit construction.

This paper is concerned with an optimization problem related to the pseudo p-Laplacian eigenproblem, with Robin boundary conditions. The principal eigenvalue is minimized over a rearrangement class generated by a fixed positive function. Existence and optimality condition are proved. The popular case where the generator is a characteristic function is also considered. In this case the method of domain derivative is used to capture qualitative features of the optimal solutions.

In this paper, we show the regularity of divergence form parabolic equations on time-dependent quasiconvex domains. The objective is to study the optimal parabolic boundary condition for the L^p estimates. The time-dependent quasiconvex domain is a generalization of the time-dependent Reifenberg flat domain, and assesses some properties analog to the convex domain. As to the a priori estimates near the boundary, we will apply the maximal function technique, Vitali covering lemma and the compactness method.

Let E be a finite-dimensional vector space over a local field, and F be its dual. For a closed subset X of E, and Y of F, consider the space D^-ξ(E; X, Y) of tempered distributions on E whose support are contained in X and support of whose Fourier transform are contained in Y. We show that D^-ξ(E; X, Y) possesses a certain rigidity property, for X, Y which are some finite unions of affine subspaces.

We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group 𝔾 (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a unitary corepresentation of 𝔾. It follows that there is an order bijection between the completely positive multipliers of L¹(𝔾) and the positive functionals on the universal quantum group . We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak*–weak*-continuous.

Among the less well-known identities established by Fay is a matrix identity which can be regarded as a vector bundle generalization of his better known trisecant identity. We show how our earlier proof of the latter can be adapted to prove his matrix identity.