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
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