复合二项K－S算子和PoissonK－S算子逼迫

Composed Binomial K-S Operators and Poisson K-S operators Approximation

引入复合二项Ｋａｎｔｏｒｏｖｉｃｈ－Ｓｔｉｅｌｔｊｅｓ算子（Ｓ＿ｒｖ）（ｘ）＝Ｓ＿（ｋ，τ）（ｘ）（τ＞０，０≤ｘ≤１），证明了当τ→＋∞时，（Ｓ＿τｖ）（ｘ）在（０，１］上几乎处处收敛于ｖ关于Ｌｅｂｅｇｕｅ测度的绝对连续部份的Ｒａｄａｎ－Ｎｉｋｏｄｙｍ导数ｆ（ｘ）．同时也证明了ＰｏｉｓｓｏｎＫ－Ｓ算子（Ｓ＿τｖ）（ｘ）＝（τｄｖ）在［ａ，ｂ］（０，＋∞）上也有类似的结论．

Let v be a finite Borel measure on[0,+∞).The Kantorovich-Stieltjesoperators of the composed binomial are defined byWhere and,the auther proves thatoperators (S_τv)converges a.e. on(0,1] to the Radan-Nikodym dirivative f(x) of theabsolutely continous part of v. From the proof of theorem,the anthor shows that for [a,b],x∈[a,b],the Poisson K-Soperators.have.