Recent developments in the theory of function spaces
Recent developments in the theory of function spaces and linear regular differential equations
Recent developments in the theory of function spaces with dominating mixed smoothness
The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...
Recent developments on the Stieltjes transform of generalized functions.
Recent progress and open questions on the numerical index of Banach spaces.
The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.
Recent progress in special Colombeau algebras: geometry, topology, and algebra
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.
Recent Results in the Theory of Matrix Transformations in Sequence Spaces
Recent trends in the field of Jordan-Banach algebras
Reciprocity theorems in the theory of representations of groups and algebras [Book]
Recognizing the topology of the space of closed convex subsets of a Banach space
Reconstruction of manifolds and subsets of normed spaces from subgroups of their homeomorphism groups [Book]
Rectangular modulus and geometric properties of normed spaces.
Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces
Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus of the normed space . The values of the rectangular modulus at some noteworthy points are well-known constants of . Characterizations (involving of inner product spaces of dimension , respectively , are given and the behaviour of is studied.
Reduced and extended weak coupling limit
The main aim of our lectures is to give a pedagogical introduction to various mathematical formalisms used to describe open quantum systems: completely positive semigroups, dilations of semigroups, quantum Langevin dynamics and the so-called Pauli-Fierz Hamiltonians. We explain two kinds of the weak coupling limit. Both of them show that Hamiltonian dynamics of a small quantum system interacting with a large resevoir can be approximated by simpler dynamics. The better known reduced weak coupling...
Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if...
Reduction of real rank in inductive limits of C*-algebras.
Reduction to dimension three of local spectra of real rank zero C*-algebras.
Reductive Algebras with Minimal Ideals.
Reelle Jordanalgebren mit endlicher Spur.
Refined Algebraic Quantization: Systems with a single constraint
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this context, on the uniqueness of the construction. While in general the results depend heavily on the choices made for certain auxiliary structures, an additional physical argument leads to a unique result for typical cases. We also discuss the 'superselection laws' that...