𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Decomposition of Polynomials with Respect to the Cyclic Group of Orderm

✍ Scribed by A. Ronveaux; A. Zarzo; I. Area; E. Godoy

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
282 KB
Volume
28
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

Given a polynomial solution of a differential equation, its m-ary decomposition, i.e. its decomposition as a sum of m polynomials P [j] (x) = k Ξ± j,k x Ξ» j,k containing only exponents Ξ» j,k with Ξ» j,k+1 -Ξ» j,k = m, is considered. A general algorithm is proposed in order to build holonomic equations for the m-ary parts P [j] (x) starting from the initial one, which, in addition, provides a factorized form of them. Moreover, these differential equations are used to compute expansions of the m-ary parts of a given polynomial in terms of classical orthogonal polynomials. As illustration, binary and ternary decomposition of these classical families are worked out in detail.

πŸ“œ SIMILAR VOLUMES

Strong asymptotics of orthogonal polynom
Strong asymptotics of orthogonal polynomials with respect to exponential weights
✍ P. Deift; T. Kriecherbauer; K. T-R McLaughlin; S. Venakides; X. Zhou πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 344 KB

We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e -Q(x) dx on the real line, where Q(x) = βˆ‘ 2m k=0 q k x k , q 2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem

Ergodicity of canonical Gibbs measures w
Ergodicity of canonical Gibbs measures with respect to the diffeomorphism group
✍ Tobias Kuna; JosΓ© Luis Silva πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 221 KB

## Abstract For general potentials we prove that every canonical Gibbs measure on configurations over a manifold __X__ is quasi‐invariant w.r.t. the group of diffeomorphisms on __X__. We show that this quasi‐invariance property also characterizes the class of canonical Gibbs measures. From this we

Decompositions of the Moonshine Module w
Decompositions of the Moonshine Module with Respect to subVOAs Associated to Codes over Z2k
✍ Hiroki Shimakura πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 145 KB

In this paper, we give decompositions of the moonshine module V with respect to subVOAs associated to extremal Type II codes over Z 2k for an integer k β‰₯ 2. Those subVOAs are isomorphic to the tensor product of 24 copies of the charge conjugation orbifold VOA. Using such decompositions, we obtain so

A Combinatorial Approach to the Double C
A Combinatorial Approach to the Double Cosets of the Symmetric Group with respect to Young Subgroups
✍ Andrew R. Jones πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 247 KB

Combinatorial methods are employed to study the double cosets of the symmetric group S n with respect to Young subgroups H and K . The current paper develops a correspondence between these double cosets and certain lists of integers . This approach leads naturally to an algorithm for computing the n

Construction of Hyperspherical Functions
Construction of Hyperspherical Functions Symmetrized with Respect to the Orthogonal and the Symmetric Groups
✍ Nir Barnea; Akiva Novoselsky πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 485 KB

We present a general recursive algorithm for the efficient construction of N-body wave functions that belong to a given irreducible representation (irrep) of the orthogonal group and are at the same time characterized by a well-defined permutational symmetry. The main idea is to construct independen