Showing papers on "Biorthogonal system published in 1973"
TL;DR: In this paper, the simplest method of calculating gravitational fields is to use a set of biorthogonal pairs of masspotential functions, and a suitable set of functions for three dimensional mass distributions is derived which uses ultraspherical polynomials.
Abstract: The simplest method of calculating gravitational fields is to use a set of biorthogonal pairs of mass-potential functions. A suitable set of functions for three dimensional mass distributions is derived which uses ultraspherical polynomials. Algorithms for computing the gravitational field are discussed which attempt to maximise computational efficiency.
74 citations
TL;DR: A Rayleigh-Schrodinger type of perturbation expansion, using a partition of the Hamiltonian into non−Hermitian parts, and biorthogonal orbitals, was developed to study excited molecular states as mentioned in this paper.
Abstract: A Rayleigh‐Schrodinger type of perturbation expansion, using a partition of the Hamiltonian into non‐Hermitian parts, and biorthogonal orbitals, is developed to study excited molecular states. In particular an expansion of the molecular interactions is defined in which all intramolecular terms cancel exactly.
38 citations
32 citations
TL;DR: In this paper, it was shown that polynomial expansions of analytic functions all correspond to essentially the same biorthogonal expansion in this sequence space and sufficient conditions for such an isometry to exist are obtained, and convergence properties of the expansions are studied.
9 citations
TL;DR: In this article, a theoretical study of spin-optimized self-consistent field methods is given in a second quantization formalism using the occupation-branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman.
Abstract: A theoretical study of the spin-optimized self-consistent field methods is given in a second quantization formalism using the occupation-branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman. A diagrammatic presentation can then be introduced. Further investigation will be thus facilitated.
4 citations
4 citations
2 citations
1 citations
TL;DR: In this paper, it was shown that if one assumes that the bases are Schauder and similar, then Theorem 1 holds for countably barrelled spaces, and this result was also proved by Dyer and Johnson [4].
Abstract: The relationship between bases and isomorphisms (i.e. linear homeomorphisms) between complete metrizable linear spaces has been studied with great interest by Arsove and Edwards (see [1] and [2]). We prove (Theorem 1) that in the case of B-complete barrelled spaces, similar generalized bases imply existence of an isomorphism. This result was also proved by Dyer and Johnson [4], so we do not give a proof. We show (Theorem 6) that if one assumes that the bases are Schauder and similar, then Theorem 1 holds for countably barrelled spaces. We use Theorem 1 to advantage (Theorems 2-5) to show that one can improve some results due to Davis [3].