Projective functors for algebraic groups

We investigate the regular subquotient category introduced by Soergel in [W. Soergel, On the relation between intersection cohomology and representation theory in positive characteristic, J. Pure Appl. Algebra 152 (1–3) (2000) 311–335]. A detailed study of projective functors enables one to relate those categories for semi-simple algebraic group G and its subgroup schemata G_rT. As an application we derive some information about the characters of tilting modules for G.     

The global Cauchy problem for the NLS and NLKG with small rough data

By using the unit-cube decomposition to the frequency spaces, we study the Cauchy problem for the nonlinear Schrödinger equation and the nonlinear Klein-Gordon equation. Some global well posedness results are obtained for the small Cauchy data in some modulation spaces .     

Periodic solutions for a class of superquadratic Hamiltonian systems

We prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second-order Hamiltonian systems by applying condition ^∗(C) to critical point theory, and some new solvability conditions of nontrivial periodic solutions are obtained.     

The convergence of three spline methods for scattered data interpolation and fitting

The convergences of three L₁ spline methods for scattered data interpolation and fitting using bivariate spline spaces are studied in this paper. That is, L₁ interpolatory splines, splines of least absolute deviation, and L₁ smoothing splines are shown to converge to the given data function under some conditions and hence, the surfaces from these three methods will resemble the given data values.     

The Koszul dual of a weakly Koszul module

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.     

The behavior of best -approximations as . A counterexample of convergence

In the space of summable sequences we give an example of a one-dimensional affine subspace C such that the best L_p-approximations of 0 from C fail to converge as p↓1. We thus give an answer to this problem of convergence in infinite measure spaces.     

On holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds

In this paper we extend some results of the paper [M. Gromov, G. Henkin, M. Shubin, Holomorphic L²-functions on coverings of pseudoconvex manifolds, Geom. Funct. Anal. 8 (1998) 552-585].     

Spectrum and analytical indices of the C-algebra of Wiener-Hopf operators

We study multivariate generalisations of the classical Wiener-Hopf algebra, which is the C^∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C^∗-algebra is known to be isomorphic to the reduced C^∗-algebra of a certain restricted action groupoid, given by the action of Euclidean space on a certain compactification. Using groupoid methods, we construct composition series for the Wiener-Hopf C^∗-algebra by a detailed study of this compactification. We compute the spectrum, and express homomorphisms in K-theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms. Namely, these symbols maps turn out to be given by an analytical family index of a continuous family of Fredholm operators. In a subsequent paper, we also obtain a topological expression of these indices.     

The algebra of harmonic functions for a matrix-valued transfer operator

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite-dimensional C^∗-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algorithms.