Fractional Functions and their Representations
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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.
KeywordsFractional 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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