reference for strongly continuous semi-groups

Question

At the moment I am trying to understand the proof of the Fredholm property in Salamon's notes on Floer homology. There I came across the notion of an unbounded operator on a (real) Hilbert space which is symmetric and does not have $0$ as an eigenvalue. It is then claimed that the operator generates strongly continuous semigroups on the respective eigenspaces.

In fact I would like to understand these notions, but I don't seem to find good introductory texts. Since the topic seems rather old googling mostly gives me very recent result which are in particular much too specific.

Can anyone give me a reference on symmetric unbounded operators on real Hilbert spaces and their corresponding semigroups?

Answer 1

Though Engel and Nagel was mentioned in the comments, the short version

http://www.fa.uni-tuebingen.de/research/publications/2006/a-short-course-on-operator-semigroups/A_Short_Course_on_Operator_Semigroups.pdf

Is a great introduction.

Answer 2

You may find it useful to look at Chapter 6 of "Linear Operators and Their Spectra" by E. Brian Davies, though he works on Banach spaces.

His book is available online.

Answer 3

You can try "Semigroups of Linear Operators and Applications to Partial Differential Equations" by Pazy.

Answer 4

For a first introduction I liked the chapters on Operator Theory and Semigroups in An Introduction to Partial Differential Equations by Rogers and Renardy. It keeps things simple, explicit and gets the main ideas across. After reading these introductory chapters other functional analysis texts will be much easier to read.