We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.

Document Type

Post-print Article

Publication Date


Publisher Statement

Copyright © 2016 American Mathematical Society.

The definitive version is available at: http://www.ams.org/books/conm/679/

Full Citation:

Garcia, Stephan Ramon, Javad Mashreghi, and William T. Ross. "Real complex functions." Contemporary Mathematics 679 (2016): 91-128.