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Complex Analysis and Operator Theory

, Volume 7, Issue 4, pp 1049–1063 | Cite as

Fractional Functions and their Representations

  • L. P. CastroEmail author
  • S. Saitoh
Article

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.

Keywords

Fractional function Best approximation Moore–Penrose generalized inverse Hilbert space Linear transform Reproducing kernel Linear mapping Convolution Norm inequality Tikhonov regularization 

Mathematics Subject Classification (2000)

Primary 46E22 Secondary 30C40 42A38 47B32 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal

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