The modulus of the boundary values of bounded analytic functions of several variables
HTML articles powered by AMS MathViewer
- by Chester Alan Jacewicz PDF
- Trans. Amer. Math. Soc. 176 (1973), 253-261 Request permission
Abstract:
One necessary condition and one sufficient condition are given in order that a nonnegative function be the modulus of the boundary values of a bounded analytic function on the polydisc. As a consequence, a weak version of a theorem of F. Riesz is generalized to several variables. For special classes of functions several conditions are given which are equivalent to a function’s being the modulus of the boundary values of a bounded analytic function. Finally, an algebraic structure is provided for these special classes of functions.References
- H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 176 (1973), 253-261
- MSC: Primary 32A10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0311931-3
- MathSciNet review: 0311931