Abstract: The classical Weyl-von Neumann theorem states that for any selfadjoint operator A in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C = C∗ such that the perturbed operator A + C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely define...

Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

This paper concerns the combinatorics of the orbit Hecke algebra associated with the orbit of a two sided Weyl group action on the Renner monoid of a finite monoid of Lie type, M . It is shown by Putcha in [12] that the Kazhdan-Lusztig involution ([6]) can be extended to the orbit Hecke algebra which enables one to define the R-polynomials of the intervals contained in a given orbit. Using the ...

We show that the Weyl group W = M 0 =M of a noncompact semisimple Lie group is obtained by taking xed point sets of smooth involutions in K=M. More precisely, one considers rst the xed point set X of the involutions deened on K=M by the elements of order 2 in exp ia. The Weyl group is either X , or the xed point set of the involutions deened on X by special elements of order 4 in exp ia.

(1) M(x) ≪ x 1 2. Conversely, the estimate M(x) ≪ x 12+ǫ implies, by partial summation, the convergence of the series ∑∞ n=1 μ(n)n −s = 1/ζ(s) for any σ > 1/2, and therefore RH. Subsequently, E. Landau [5] showed that, assuming RH, (1) is valid with ǫ ≪ log log log x/ log log x, and E.C. Titchmarsh [13] improved this to ǫ ≪ 1/ log log x. H. Maier and H.L. Montgomery [7] obtained a substantial i...

The notion of convergent star product is generally understood as the data of a one parameter family {Et}t∈I ⊂ C∞(M) of function algebras on a Poisson manifold (M, { , }). On each of them one is given an associative algebra structure ⋆t which respect to which the function space Et is closed. The family of products {⋆t} should moreover define in some sense a deformation of the commutative pointwi...