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- W852030609 endingPage "70" @default.
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- W852030609 abstract "The term “Algebraic Analysis” in the last two decades is used in two completely different senses. It seems that at least one is far away from its historical roots. Thus, in order to explain this misunderstanding, the history of this term from its origins is recalled. The term “Analyse Algebrique” (“Algebraic Analysis”) in the last two decades is used in two completely different senses. It seems that at least one is far away from its historical roots. Thus, in order to explain this misunderstanding, I would like to recall the history of this term from its origins. The term “Algebraic Analysis” was initially used by Lagrange two hundred years ago in the title of his book (cf. References, [1797-1813]) in order to point out that most of results have been obtained by algebraic operations on analytic quantities. As we shall see later, in that general and common sense this name was used in the 19th and 20th century. To begin with, we should explain what is meant by Algebraic Analysis at present (cf. Encyclopaedia of Mathematics, [1997]). The main idea of Algebraic Analysis in its present, more strict, sense derives from the fact that the differential operator D = d dt is right invertible in several function spaces. Foundations of Algebraic Analysis are the following: Let L(X) be the set of all linear operators with domains and ranges in a linear space X (in general, without any topology) over a field F of scalars with characteristic zero and let L0(X) = {A ∈ L(X) : dom A = X}. Let R(X) be the set of all right invertible operators in L(X). Let D ∈ R(X). Let RD ⊂ L0(X) be the set of all right inverses for D, i.e. DR = I (identity operator) if R ∈ RD (i.e. the Leibniz-Newton formula holds: d dt ∫ t a f(s)ds = f(t) for all functions f from the space under consideration). Moreover, dom D = RX ⊕ ker D. For all R,R′ ∈ 2000 Mathematics Subject Classification: 01-00, 01A55, 01A60, 00A20." @default.
- W852030609 created "2016-06-24" @default.
- W852030609 creator A5031365325 @default.
- W852030609 date "2000-01-01" @default.
- W852030609 modified "2023-09-26" @default.
- W852030609 title "Two centuries of the term algebraic analysis" @default.
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