Numbering and notation

1. List of symbols: The list of symbols is incorporated as part of the index and

can be found at the end of the book.

2. Definitions: When defining functions, sets, operators, etc., we will often use

the notation A := xxx. By this we mean A 'is defined to be' xxx.

3. Estimates: We use the notation A x B to mean there are (positive) con-

stants c\ and C2 such that

c\A B c2A.

As is traditional in analysis, the constants c\ and c2 can change from one

line to the next.

4. Closures vs. conjugates: For a set A C C, we use A to denote the complex

conjugates of the points in A. For a set U in some topological vector space,

we use U~ to denote the closure of U.

5. Manifold vs. subspace: If U (as above) is closed under the vector space

operations, we will say that U is a 'linear manifold'. A 'subspace' will be a

closed linear manifold.

6. Numbering: Numbering is done by chapter and section, and all equations,

theorems, propositions, and such are numbered consecutively.

7. Errors: Though we have made every attempt to avoid any errors, we realize

that we are probably not perfect. We will maintain a list of corrections

(mathematical, attributions, etc.) which the reader can find off Ross' web

page at

www.richmond.edu/~wross

Please feel free to contact us with your comments.

Joseph A. Cima

Department of Mathematics

University of North Carolina, Chapel Hill

Chapel Hill, North Carolina 27599

cimaOmath.. unc. edu

William T. Ross

Department of Mathematics and Computer Science

University of Richmond

Richmond, Virginia 23173

wross@richmond.edu

XI