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Some Remarks on Functional Analysis

Blowey, James F.; Straughan, Brian

Some Remarks on Functional Analysis Thumbnail


Brian Straughan


Richard B. Hetnarski


Functional analysis is a key tool in the study of partial differential equations which helps to answer key questions such as existence, well-posedness, and the class in which a solution should belong. We begin these remarks by introducing normed spaces and Banach spaces and then bounded linear operators in normed spaces. Next, we define Hilbert spaces and consider aspects relating to linear operators on Hilbert spaces. With this structure, we are able to consider well-posed of problems and describe the notions of Hölder and Lyapunov stability and Hadamard well-posedness. Finally, we describe how some thermal stress problems can be formulated using abstract operator notation.


Blowey, J. F., & Straughan, B. (2014). Some Remarks on Functional Analysis. In R. B. Hetnarski (Ed.), Encyclopedia of Thermal Stresses. Springer Verlag.

Publication Date 2014
Deposit Date Oct 26, 2021
Publicly Available Date Oct 27, 2021
Publisher Springer Verlag
Book Title Encyclopedia of Thermal Stresses
ISBN 9789400727380


Accepted Book Chapter (141 Kb)

Copyright Statement
This a post-peer-review, pre-copyedit version of a chapter published in Encyclopedia of Thermal Stresses. The final authenticated version is available online at:

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