Functional Analysis: Fundamentals and Applications

ISBN-13: 9781489987945 / Angielski / Miękka / 2015 / 213 str.

Michel Willem

Opis

This book presents the principles of functional analysis. It includes recent simple proofs of the isoperimetric and the Faber-Krahn inequality, an elementary introduction to capacity theory, and a new perspective on the history of functional analysis.

Recenzje

From the reviews:

"The book is a very good contribution to the literature in a classical field of analysis. It should be of interest to specialists in pure and applied functional analysis and it can be used by advanced graduate students whom it will bring to the forefront of research. The book also serves to prepare the student for more advanced topics in analysis, especially the modern theory of partial differential equations." (Teodora-Liliana Radulescu, zbMATH, Vol. 1284, 2014)

Spis treści

​Preface.- The Integral.- Norm.- Lebesgue Spaces.- Duality.- Sobolev Spaces.- Capacity.- Elliptic Problems.- Appendix.- Epilogue.- References.- Index of Notations.- Index.

Blurb

The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional  analysis, in relation with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics.