Research Areas

A major theme of my research is Fractal Interpolation Theory. I have contributed to the development of several classes of fractal interpolation functions, including coalescence hidden-variable fractal interpolation functions, super fractal interpolation functions, and, more recently, Edelstein hiddenvariable fractal interpolation functions. My work investigates their construction, smoothness properties, stability, dimension theory, wavelet representations, fractional calculus, and approximation capabilities. These studies provide flexible mathematical tools for modelling irregular data and complex geometric structures.

Another active area of my research concerns self-affine measures and fractal measure theory. In collaboration with students and researchers, I study spectral properties of self-affine measures, orthogonal exponential systems, and questions related to spectrality and harmonic analysis on fractal measures. These investigations contribute to a deeper understanding of the interplay between geometric structure, measure-theoretic properties, and Fourier analysis.

I am also interested in the analysis of fractals, particularly harmonic functions, energy forms, and the dimensional properties of functions defined on post-critically finite fractals such as the Sierpinski gasket and the Vicsek fractal. Recent work from my group explores harmonic functions on higher dimensional fractals, energy structures, and the geometric complexity of their graphs through box-counting and related dimensions.

In addition, I work on labyrinth fractals. These fascinating self-similar structures exhibit intricate pathways and rich geometric properties, making them a natural setting for studying connectivity, dimension, and topological complexity in fractal spaces. My work has focused on the construction and analysis of new classes of labyrinth fractals, including labyrinth fractals on convex quadrilaterals and sequential labyrinth fractals. Through these investigations, I explore how geometric transformations and iterative construction rules influence the resulting fractal structure. This research contributes to a deeper understanding of self-similar geometry and provides new examples of fractal sets with complex path structures and intriguing analytical properties.