Interpolation in a classical Hilbert space of entire functions

Author:
Robert M. Young

Journal:
Trans. Amer. Math. Soc. **192** (1974), 97-114

MSC:
Primary 30A98; Secondary 30A80, 46E20

DOI:
https://doi.org/10.1090/S0002-9947-1974-0357823-6

MathSciNet review:
0357823

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *H* denote the Paley-Wiener space of entire functions of exponential type which belong to on the real axis. A sequence of distinct complex numbers will be called an *interpolating sequence* for *H* if , where *T* is the mapping defined by . If in addition is a set of uniqueness for *H*, then is called a *complete interpolating sequence*. The following results are established. If and if the imaginary part of is sufficiently small, then is an interpolating sequence. If and if the imaginary part of is uniformly bounded, then is a complete interpolating sequence and is a basis for . These results are used to investigate interpolating sequences in several related spaces of entire functions of exponential type.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0357823-6

Keywords:
Paley-Wiener space,
interpolating sequence,
complete interpolating sequence,
nonharmonic Fourier series expansion,
entire functions of exponential type

Article copyright:
© Copyright 1974
American Mathematical Society