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Favard Operators
In functional analysis, a branch of mathematics, the Favard operators are defined by: : mathcal_n(f)x) = \frac \sum_^\infty where x\in\mathbb, n\in\mathbb. They are named after Jean Favard. Generalizations A common generalization is: : mathcal_n(f)x) = \frac \sum_^\infty where (\gamma_n)_^\infty is a positive sequence that converges to 0. This reduces to the classical Favard operators when \gamma_n^2=1/(2n). References * This paper also discussed Szász–Mirakyan operator In functional analysis, a discipline within mathematics, the Szász–Mirakyan operators (also spelled "Mirakjan" and "Mirakian") are generalizations of Bernstein polynomials to infinite intervals, introduced by Otto Szász in 1950 and G. M. Mira ...s, which is why Favard is sometimes credited with their development (e.g. Favard–Szász operators Footnotes Approximation theory {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |