The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^\infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H…
Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's inte…
The book is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for $H^\infty$, and t…
"The book is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for H[superscript [i…
Review text: "M. does an admirable job by serving both purposes, remaining concise and methodologically accurate on the one hand and writing in a very readable and interesting style on the other. Consequently, for the scholar, the advanced student, and the learned non-specialist…
Metric spaces, equivalent spaces, classification of subsets, and the space of fractals; Transformations on metric spaces, contraction mappings and the construction of fractals; Chaotic dynamics on fractals; Fractal dimension; fractal interpolation; Julia sets; Parameter spaces a…