Around operators not increasing the degree of polynomials

Autor:	Mesquita, T. Augusta, Maroni, P.
Rok vydání:	2016
Předmět:	Mathematics - Classical Analysis and ODEs 42C05 33C45 33D45
Druh dokumentu:	Working Paper
Popis:	We present a generic operator $J$ simply defined as a linear map not increasing the degree from the vectorial space of polynomial functions into itself and we address the problem of finding the polynomial sequences that coincide with the (normalized) $J$-image of themselves. The technique developed assembles different types of operators and initiates with a transposition of the problem to the dual space. It is also provided examples where the results are applied to the case where $J$'s expansion is limited to three terms. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1609.04540 Zobrazit plný text záznamu View this record from Arxiv