“Baskakov operator”的意思、由来-开放百科全书

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Baskakov operator

释义

Basic results
References
Footnotes

In functional analysis, a branch of mathematics, the Baskakov operators are generalizations of Bernstein polynomials, Szász–Mirakyan operators, and Lupas operators. They are defined by

where ( can be ), , and is a sequence of functions defined on that have the following properties for all :

. Alternatively, has a Taylor series on .
is completely monotone, i.e. .
There is an integer such that whenever

They are named after V. A. Baskakov, who studied their convergence to bounded, continuous functions.^[1]

Basic results

The Baskakov operators are linear and positive.^[2]

References

{{cite journal| last=Baskakov | first=V. A. | year=1957 | script-title=ru:Пример последовательности линейных положительных операторов в пространстве непрерывных функций |trans-title=An example of a sequence of linear positive operators in the space of continuous functions | journal=Doklady Akademii Nauk SSSR | language=Russian | volume=113 | pages=249–251}}

Footnotes

1. ^{{cite encyclopedia|last=Agrawal|first=P. N.|editor=Michiel Hazewinkel|year=2001|title=Baskakov operators|encyclopedia=Encyclopaedia of Mathematics|publisher=Springer|isbn=1-4020-0609-8|url=http://eom.springer.de/b/b110150.htm}}
2. ^{{cite encyclopedia|last=Agrawal|first=P. N.|author2=T. A. K. Sinha|editor=Michiel Hazewinkel|year=2001|title=Bernstein–Baskakov–Kantorovich operator|encyclopedia=Encyclopaedia of Mathematics|publisher=Springer|isbn=1-4020-0609-8|url=http://eom.springer.de/b/b110350.htm}}

1 : Approximation theory

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