Reproducing Kernel Hilbert Space and Coalescence Hidden-variable Fractal Interpolation Functions

Abstract

Reproducing Kernel Hilbert Spaces (RKHS) and their kernel are important tools which have been found to be incredibly useful in many areas like machine learning, complex analysis, probability theory, group representation theory and the theory of integral operator. In the present paper, the space of Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is demonstrated to be an RKHS and its associated kernel is derived. This extends the possibility of using this new kernel function, which is partly self-affine and partly non-self-affine, in diverse fields wherein the structure is not always self-affine.

Keywords

• fractal
• interpolation
• coalescence
• attractor
• reproducing kernel
• hilbert space
• 42c40
• 41a15
• 65t60
• 42c10
• 28a80