NLS in the Modulation Space $$M_{2,q}({mathbb {R}})$$ M 2 , q ( R )

Journal of Fourier Analysis and Applications - We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in the...     

Volumes for $${mathrm{SL}}_N({mathbb {R}})$$ , the Selberg Integral and Random Lattices

Foundations of Computational Mathematics - There is a natural left and right invariant Haar measure associated with the matrix groups GL $${}_N(mathbb {R})$$ and SL $${}_N(mathbb {R})$$ due to...     

Gabor Frames in $${\ell }^2({\mathbb {Z}})$$ ℓ 2 ( Z ) and Linear Dependence

We prove that an overcomplete Gabor frame in \({\ell }^2({\mathbb {Z}})\) generated by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in \({\ell }^2({\mathbb {Z}})\) with modulation parameter 1 / M and translation parameter N for some \(M,N\in {\mathbb {N}},\) and generated by a finite sequence g in \({\ell }^2({\mathbb {Z}})\) with K nonzero entries.

     

On the generalized $$text {SO}(2n,{{mathbb {C}}})$$ SO ( 2 n,C ) -opers

Annals of Global Analysis and Geometry - Since their introduction by Beilinson–Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin’s integrable system and Hecke...     

Trace-free $$mathrm{SL}(2,{pmb {mathbb {C}}})$$ SL ( 2 , C ) -representations of arborescent links

Periodica Mathematica Hungarica - Given a link $$Lsubset S^3$$ , a representation $$pi _1(S^3-L)rightarrow mathrm{SL}(2,{mathbb {C}})$$ is trace-free if it sends each meridian to an element...     

Surfaces in $${\mathbb{S}^2\times\mathbb{R}}$$ with a canonical principal direction

We show a way to choose nice coordinates on a surface in and use this to study minimal surfaces. We show that only open parts of cylinders over a geodesic in are both minimal and flat. We also show that the condition that the projection of the direction tangent to onto the tangent space of the surface is a principal direction, is equivalent to the condition that the surface is normally flat in . We present classification theorems under the extra assumption of minimality or flatness. J. Fastenakels is a research assistant of the Research Foundation—Flanders (FWO). J. Van der Veken is a postdoctoral researcher supported by the Research Foundation—Flanders (FWO). This work was partially supported by project G.0432.07 of the Research Foundation—Flanders (FWO).     

Ideal Structure and Stable Rank of $${mathbb {C} e+ ell^2(I)}$$ with the Hadamard Product

Let I be any index set. We consider the Banach algebra mathbb C e+ l²(I){mathbb {C} e+ ell^2(I)} with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize divisors, maximal ideals, closed ideals and closed principal ideals. For I=mathbb N{I=mathbb {N}} we also characterize all prime z-ideals in this Banach algebra.     

Maps from M2({\mathbb{F}}) to M3({\mathbb{F}}) that are multiplicative with respect to the Jordan triple product

We characterize the Jordan triple product preserving maps M₂( ${\mathbb{F}}$ ) to M₃( ${\mathbb{F}}$ ) for algebraically closed fields ${\mathbb{F}}$ , char ${\mathbb{F} \neq 2}$ .     

Embedding some Riemann surfaces into $${\mathbb {C}^2}$$ with interpolation

We prove that several types of open Riemann surfaces, including the finitely connected planar domains, embed properly into such that the values on any given discrete sequence can be arbitrarily prescribed. Kutzschebauch supported by Schweizerische Nationalfonds grant 200021-107477/1.     

Height estimates for constant mean curvature graphs in $$mathrm {Nil}_3$$Nil3 and $${widetilde{PSL_2}}({mathbb {R}})$$PSL2~(R)

Archiv der Mathematik - In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces $$mathrm {Nil}_3$$ and...     

On the Intersection of $$$$-Complete Open Subsets with $$\mathcal {C}^2$$C2 Boundary in $$\mathbb {C}^n$$Cn

We prove that in \(\mathbb {C}^n\), the intersection of finitely many open, relatively compact, \((n-1)\)-complete subsets with \(\mathcal {C}^2\) boundary for which every two boundaries intersect transversally, is cohomologically \((n-1)\)-complete.     

Two-Wavelet Localization Operators on $$ L^p(\mathbb{R}^n) $$ for the Weyl-Heisenberg Group

We give results on the boundedness and compactness of localization operators with two admissible wavelets on for the Weyl-Heisenberg group.     

On the Biharmonic Curves in the Special Linear Group $${{mathbf{SL}}{bf (2},{mathbb{R}}{bf )}}$$

Mediterranean Journal of Mathematics - We characterize the biharmonic curves in the special linear group $${mathrm{SL}(2,{mathbb{R}})}$$ . In particular, we show that all proper biharmonic curves...     

Jackson inequality in L2($$ \mathbb{T}^N $$) with generalized modulus of continuity

The sharp Jackson inequality is proved for the space of periodic functions of many variables with a mean-square norm for an arbitrary modulus of continuity generated by a difference operator with constant coefficients.     

Discrete Orbits,Recurrence and Solvable Subgroups of $${{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}$$

We discuss the local dynamics of a subgroup of \({{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}\) possessing locally discrete orbits as well as the structure of the recurrent set for more general groups. It is proved, in particular, that a subgroup of \({{\mathrm{Diff}}\, ({{\mathbb {C}}}^2, 0)}\) possessing locally discrete orbits must be virtually solvable. These results are of considerable interest in problems concerning integrable systems.