On the nonexistence of unimodular functions in $R^{2}(X, dx dy)$
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- by Alfred G. Brandstein PDF
- Proc. Amer. Math. Soc. 49 (1975), 339-341 Request permission
Abstract:
It is shown for certain planar sets, e.g., Brennan sets, with no interior, that if $f \in {R^2}(X,dxdy)$ and $|f| = 1\; \text {a.e.}\; dxdy$ then $f \equiv \text {constant}$ .References
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A. G. Brandstein, Function spaces related to hypo-Dirichlet algebras, Doctoral Dissertation, Brown University, Providence, R. I., 1972.
- James E. Brennan, Invariant subspaces and rational approximation, J. Functional Analysis 7 (1971), 285–310. MR 0423059, DOI 10.1016/0022-1236(71)90036-x —, Approximation in the mean and quasi-analyticity, University of Kentucky, Math. Dept., 1972.
- Kenneth Hoffman and Hugo Rossi, Extensions of positive weak$^{\ast }$-continous functionals, Duke Math. J. 34 (1967), 453–466. MR 225168
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 339-341
- MSC: Primary 46E15; Secondary 30A98
- DOI: https://doi.org/10.1090/S0002-9939-1975-0367632-6
- MathSciNet review: 0367632