Hilbert Space Methods in Science and Engineering

This book aims to make Hilbert space theory accessible to applied mathematicians, engineers and scientists. Based on the author's courses on functional analysis for engineering students, all that is assumed is a knowledge of linear algebra and analysis. The book covers theoretical fundamentals, the geometry of Hilbert spaces, the reproduction of kernel Hilbert spaces and operator theory, including causal operators. The construction of mathematical models using Hilbert space theory is emphasized and the results which follow from these models are evaluated. In particular, mathematical models based on reproducing kernel Hilbert spaces and causal operators are presented here at an introductory level.