The calculus of fractal interpolation functions
Journal of Approximation Theory
Multiresolution analyses based on fractal functions
Journal of Approximation Theory
Kernel Principal Component Analysis
ICANN '97 Proceedings of the 7th International Conference on Artificial Neural Networks
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Generalized Cubic Spline Fractal Interpolation Functions
SIAM Journal on Numerical Analysis
Pattern Recognition, Fourth Edition
Pattern Recognition, Fourth Edition
RKHS approach to detection and estimation problems--I: Deterministic signals in Gaussian noise
IEEE Transactions on Information Theory
Some relations among RKHS norms, Fredholm equations, and innovations representations
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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Reproducing Kernel Hilbert Spaces (RKHSs) are a very useful and powerful tool of functional analysis with application in many diverse paradigms, such as multivariate statistics and machine learning. Fractal interpolation, on the other hand, is a relatively recent technique that generalizes traditional interpolation through the introduction of self-similarity. In this work we show that the functional space of any family of (recurrent) fractal interpolation functions ((R)FIFs) constitutes an RKHS with a specific associated kernel function, thus, extending considerably the toolbox of known kernel functions and introducing fractals to the RKHS world. We also provide the means for the computation of the kernel function that corresponds to any specific fractal RKHS and give several examples.