Mathematical Analysis: Linear and Metric Structures and Continuity

Mariano Giaquinta, Giuseppe Modica, "Mathematical Analysis: Linear and Metric Structures and Continuity"

Birkhäuser Boston; 1 edition (September 4, 2007) | ISBN: 0817643753 | 470 pages | PDF | 17,1 Mb

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.