Volume 116, Issue 3
August 2006, pages 257-371
pp 257-266
𝑛-Colour Self-Inverse Compositions
MacMahon’s definition of self-inverse composition is extended to 𝑛-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.
pp 267-270
Maximally Differential Ideals in Regular Local Rings
It is shown that if 𝐴 is a regular local ring and 𝐼 is a maximally differential ideal in 𝐴, then 𝐼 is generated by an 𝐴-sequence.
pp 271-291
On the Classification of Complex Vector Bundles of Stable Rank
Constantin Bǎnicǎ Mihai Putinar
One describes, using a detailed analysis of Atiyah–Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle.
pp 293-298
Pro-Torus Actions on Poincaré Duality Spaces
In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if `torus’ is replaced by `pro-torus’.
pp 299-316
On CNC Commuting Contractive Tuples
T Bhattacharyya J Eschmeier J Sarkar
The characteristic function has been an important tool for studying completely non-unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space $\mathcal{H}$. We show that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in $\mathbb{C}^n$, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.
pp 317-323
Joint Local Quasinilpotence and Common Invariant Subspaces
In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for 𝑁-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].
pp 325-336
Inequalities Involving Upper Bounds for Certain Matrix Operators
In this paper, we considered the problem of finding the upper bound Hausdorff matrix operator from sequence spaces $l_p(v)$ (or $d(v,p)$) into $l_p(w)$ (or $d(w, p)$). Also we considered the upper bound problem for matrix operators from $d(v,1)$ into $d(w,1)$, and matrix operators from $e(w,∞)$ into $e(v,∞)$, and deduce upper bound for Cesaro, Copson and Hilbert matrix operators, which are recently considered in [5] and [6] and similar to that in [10].
pp 337-360
Sobolev Spaces Associated to the Harmonic Oscillator
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= -𝛥 + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
pp 361-371
The recently suggested embedding method to solve linear boundary value problems is here extended to cover situations where the domain of interest is unbounded or multiply connected. The extensions involve the use of complete sets of exterior and interior eigenfunctions on canonical domains. Applications to typical boundary value problems for Laplace’s equation, the Oseen equations and the biharmonic equation are given as examples.
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