Linear Operator Theory in Engineering and Science

by Arch W.;Sell Naylor

This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.

Genres: Mathematics

624 pages, Hardcover

First published November 30, 1970

Reviews

[HikBook]

Topological structure Example 13 (page 52): It is define the space of all functions x(s) on a vertical line such that int_{vertical line} |x(s)|^2ds is finite. This space is a metric space.
(IMPORTANT role in Fourier and Laplace transform)

El Teorema 3.13.6 dice que, la completitud, es preservada mediante isometrías.

12. Functions of operators (operational calculus)
Let T a compact normal operator on H and T=sum_n lambda_n P_n (spectral theorem)
T^2 is also compact and T^2=sum_n lambda_n ^2P_n (T^n idem)


If f(z) is continuous defined on the spectrum(T) then
f(T)=sum_n f(lambda_n)P_n [Dunford and Schwartz, Simmons Taylor]

Fractional T^{1/2}=sum_n lambda_n^{1/2}P_n

5.22 adjoint operator
Example 4: The Volterra integral operators is a causal operator. The adjoint operator is a anticausal operator.


Theorem 5.22.8 Let operators Pu=i D_x u and Qu=xu with domains D(P)={u in L^2(R): u absolutely continuous and u' in L^2(R)}, D(Q)={u in L^2(R): xu in L^2(R)}
Then the fourier transforms F is a one to one corrrespondence between D(P and D(Q) moreover
P=FQF^{-1} and Q=F^{-1}PF

Exercise 14. If u is in D(Q) then u in L^1(R)

[Ben · Rating 4 out of 5]

Concise, but with excellent examples and well thought out problems.