Two Hilbert spaces in which polynomials are not dense
Authors: D. J. Newman and D. K. Wohlgelernter
Journal: Trans. Amer. Math. Soc. 168 (1972), 67-72
MSC: Primary 30A82
MathSciNet review: 0294655
Abstract: Let be the Hilbert space of entire functions such that , where is a positive measure defined on the Borel sets of the complex plane. Two Hilbert spaces are constructed in which polynomials are not dense. In the second example, our space is one which contains all exponentials and yet in which the exponentials are not complete. This is a somewhat surprising result since the exponentials are always complete on the real line.
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