Riemann’s Boundary Problem with Infinite Index

The book gives the first complete presentation of two closely connected subjects that are now used in various branches of complex analysis. In the first part the theory of analytic functions of completely regular growth in an angle is developed. Being a natural extension of the classical theory of entire functions of completely regular growth, this theory possesses principally new features due to the influence of boundary values on the sides of the angle. The second part contains the theory of the Riemann boundary value problem with power type infinite index. Using the results obtained in the first part of the book, the author gives complete and efficient solutions to the problem in various natural classes of analytic functions. The solution to the well-known Paley problem on the growth of entire functions of finite order is given as one possible application.