Logarithmic residues, generalized idempotents, and sums of idempotents in Banach algebras

In a commutative Banach algebraB the set of logarithmic residues (i.e., the elements that can be written as a contour integral of the logarithmic derivative of an analyticB-valued function), the set of generalized idempotents (i.e., the elements that are annihilated by a polynomial with non-negative integer simple zeros), and the set of sums of idempotents are all the same. Also, these (coinciding) sets consist of isolated points only and are closed under the operations of addition and multiplication. Counterexamples show that the commutativity condition onB is essential. The results extend to logarithmic residues of meromorphicB-valued functions.     

Rank decomposition in zero pattern matrix algebras

For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H.Bart, A.P.M.Wagelmans (2000). The proof involves elements from integer programming and employs Farkas’ lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred to above can be extended to other zero pattern matrix algebras. It is shown that such a generalization does indeed hold for certain digraphs determining the pattern of zeros. The digraphs in question can be characterized in terms of forests, i.e., disjoint unions of rooted trees.     

Surface quantum oscillations in accumulation and inversion layers on tellurium

Surface quantum oscillations of the Shubnikov—de Haas type have been recorded in (1$\text{1}$00) planes of p-type accumulation and n-type inversion layers of tellurium. Two electric subbands are found in accumulation, which can be explained rather well on the basis of an exponential potential well. In strong inversion layers three subbands are observed. It is not yet clear, whether they must be attributed to the H₆ conduction band minimum of tellurium or whether another band minimum is involved.     

Some remarks on the asymptotic behavor of toeplitz determinants

In order to optimize the stability regions we construct families of k multi-step methods with free parameters and of order k+1. We exhibit parameters for which the real interval of stability is arbitrarly large and using the Flexible Tolerance Method we show how these parameters optimize - under a predefined criterion - the stability region. Computational experience, while limited, has indicated that the procedure is efficient     

Algebras of Approximation Sequences: Finite Sections of Band-Dominated Operators

We develop the stability theory for the finite section method for general band-dominated operators on l^p spaces over Z^k. The main result says that this method is stable if and only if each member of a whole family of operators – the so-called limit operators of the method – is invertible and if the norms of these inverses are uniformly bounded.     

Fredholm theory and finite section method for band-dominated operators

The topics of this paper are Fredholm properties and the applicability of the finite section method for band operators onl ^p -spaces as well as for their norm limits which we call band-dominated operators. The derived criteria will be established in terms of the limit operators of the given band-dominated operator. After presenting the general theory, we present its specifications to concrete classes of band-dominated operators.To the memory of Professor Mark KreinSupported by the DFG grant 436 RUS/17/148/95Supported by a DFG Heisenberg grant     

Multiaxial miniaturized load cell for measuring forces acting through a sternotomy

Experimental Techniques - A miniaturized multiaxial load cell was developed and calibrated. The transducer geometry was designed for sternal closure following sternotomy. The overall accuracy was...