An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking” and “boundedly complete” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. ...

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product ⊗n s,μX, for any symmetric tensor norm μ. In addi...

Lascoux stated that the type A Kostka-Foulkes polynomials K?,?(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, former polynomial is a t-analogue multiplicity dominant weight ? irreducible representation highest ?. We formulate decomposition arbitrary type, and view it as strengthening monotonicity K?,?(t). also define combinatorial version decompos...

Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions ...

In this thesis, new methodology of computing properties aimed for multiple applications is developed. We use quantum mechanics to compute properties of molecules, and having these properties as a basis, we set up equations based on a classical reasoning. These approximations are shown to be quite good in many cases, and makes it possible to calculate linear and non-linear properties of large sy...