An Integral Representation of a Family of Slit Mappings

DOI: 10.4236/apm.2012.23028   PDF   HTML     2,941 Downloads   5,554 Views  

Abstract

We consider a normalized family F of analytic functions f, whose common domain is the complement of a closed ray in the complex plane. If f(z) is real when z is real and the range of f does not intersect the nonpositive real axis, then f can be reproduced by integrating the biquadratic kernel against a probability measure u(t) . It is shown that while this integral representation does not characterize the family F, it applies to a large class of functions, including a collection of functions which multiply the Hardy space Hp into itself.

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A. Cartier and M. Sterner, "An Integral Representation of a Family of Slit Mappings," Advances in Pure Mathematics, Vol. 2 No. 3, 2012, pp. 200-202. doi: 10.4236/apm.2012.23028.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[5] P. L. Duren, “Theory of Hp Spaces,” Academic Press, New York, 1970.

  
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