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Fractional Functions and their Representations

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Abstract

For arbitrary non-identically zero functions f, we will introduce some natural fractional functions f 1 having f as denominators and we shall consider their representations f 1 by appropriate numerator functions within a reproducing kernel Hilbert spaces framework. That is, in the present work we would like to introduce very general fractional functions (e.g., having the possibility of admitting zeros in their denominators) by means of the theory of reproducing kernels.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810–193, Aveiro, Portugal

    L. P. Castro & S. Saitoh

Authors
  1. L. P. Castro
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  2. S. Saitoh
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Correspondence to L. P. Castro.

Additional information

Communicated by Daniel Aron Alpay.

This work was supported in part by Center for Research and Development in Mathematics and Applications of University of Aveiro, and the Portuguese Science Foundation (FCT–Fundação para a Ciência e a Tecnologia). The second author is also supported in part by the Grant-in-Aid for the Scientific Research (C)(2)(No. 21540111) from the Japan Society for the Promotion Science.

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Castro, L.P., Saitoh, S. Fractional Functions and their Representations. Complex Anal. Oper. Theory 7, 1049–1063 (2013). https://doi.org/10.1007/s11785-011-0154-1

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  • DOI: https://doi.org/10.1007/s11785-011-0154-1

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