The generalized inverses of differentiation and integration

Autor:	Steven H. Weintraub
Rok vydání:	2021
Předmět:	Combinatorics Degree (graph theory) General Mathematics Operator (physics) Product (mathematics) Legendre polynomials Vector space Mathematics
Zdroj:	Expositiones Mathematicae. 39:679-682
ISSN:	0723-0869
DOI:	10.1016/j.exmath.2021.07.004
Popis:	Let P n be the vector space of polynomials of degree at most n , equipped with the inner product 〈 f , g 〉 = ∫ − 1 1 f ( x ) g ( x ) d x . Let D : P n ⟶ P n − 1 be the differentiation operator and I : P n − 1 ⟶ P n be the integration operator. In this paper the generalized (Moore–Penrose) inverses of D and I are computed. The answer for D is straightforward, though perhaps somewhat unexpected. The answer for I requires more work, and involves Legendre polynomials in an unexpected way.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::889bdebfe6ec019cd1f5ccbe30033cb3 https://doi.org/10.1016/j.exmath.2021.07.004 Zobrazit plný text záznamu Full Text from ScienceDirect