Spaces of Real-Valued Functions
This chapter is a brief background on spaces of continuous functions and some Sobolev spaces including basic properties, embedding theorems and trace theorems. We recall some classical definitions and theorems of functional analysis which will be used throughout this work. These results are standard and so they are stated without proofs; details and proofs can be found in to many references. We only deal with real valued functions. We assume that the reader is familiar with the basic concepts of general topology and functional analysis.
KeywordsHilbert Space Banach Space Sobolev Space Fractional Order Dual Space