Notes on ordered reproducing Hilbert spaces over the complex plane |
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Authors: | Shengzhao Hou Xianmin Xu |
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Institution: | a Department of Mathematics, Suzhou University, Suzhou 215006, PR China b Institute of Mathematics, Jiaxing College, Jiaxing 314001, PR China |
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Abstract: | Let f, g be entire functions. If there exist M1,M2>0 such that |f(z)|?M1|g(z)| whenever |z|>M2 we say that f?g. Let X be a reproducing Hilbert space with an orthogonal basis . We say that X is an ordered reproducing Hilbert space (or X is ordered) if f?g and g∈X imply f∈X. In this note, we show that if then X is ordered; if then X is not ordered. In the case , there are examples to show that X can be of order or opposite. |
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Keywords: | Reproducing Hilbert space Ordered reproducing Hilbert space |
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