The sharp Sobolev inequality in quantitative form
The Shirali-Ford theorem as a consequence of Ptak theory for hermitian Banach algebras
A simple application of Pták theory for hermitian Banach algebras, combined with a result on normed Q-algebras, gives a non-technical new proof of the Shirali-Ford theorem. A version of this theorem in the setting of non-normed topological algebras is also provided.
The short-range expansion in solid state physics
The short-time propagator and the boundary conditions in the quantum mechanics
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The simplex of tracial quantum symmetric states
We show that the space of tracial quantum symmetric states of an arbitrary unital C*-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C*-algebra free product of A with itself infinitely many times. We also show that the extreme points of this simplex are dense, making it the Poulsen simplex when A is separable and nontrivial. In the course of the proof we characterize the centers of certain tracial amalgamated free product C*-algebras.
The simplicity of the quotient algebra M(A)/A of a simple C*-algebra.
The simultaneous existence of linear functionals
The singular set of the minima of certain quadratic functionals
The Słodkowski spectra and higher Shilov boundaries
We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
The Small Ball Theorem for Hilbert Spaces.
The Sobolev capacity on metric spaces.
The Sobolev embeddings are usually sharp.
The Sobolev spaces of harmonic functions
The Sobolev-Besov imbedding theorem from the viewpoint of semi-groups of operators
The Sobolev-Il'in theorem for the -Riesz potential.
The socle and finite-dimensionality of a semiprime Banach algebra
The solution of a minimax problem connected to the irreducibility of polynominals.
The solution of embedding problems in the framework of GAPs with applications on nonlinear PDEs.
The space bv(p), its β-dual and matrix transformations.