Functional Analysis in Applied Mathematics and Engineering

ISBN-13: 9780367399412 / Angielski / Miękka / 2019 / 312 str.

Michael Pedersen

Opis

Functional Analysis in Applied Mathematics and Engineering focuses on material useful to control specialists working in the disciplines of electrical, mechanical, and aerospace engineering. It begins with a rigorous introduction to the abstract basic function spaces and operators, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time-dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.

Spis treści

Topological and Metric Spaces
Banach Spaces
Bounded Operators
Hilbert Spaces
Operators in Hilbert Space
Spectral Theory
Integral Operators
Semigroups of Evolution
Sobolev Spaces
Interpolation Spaces
Linear Elliptic Operators
Regularity of Hyperbolic Mixed Problems
The Hilbert Uniqueness Method
Exercises
References

O autorze

Pedersen, Michael