## An Introduction to Nonharmonic Fourier SeriesAn Introduction to Nonharmonic Fourier Series |

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### Contents

1 | |

Chapter 2 Entire Functions of Exponential Type | 53 |

Chapter 3 The Completeness of Sets of Complex Exponentials | 111 |

Chapter 4 Interpolation and Bases in Hilbert Space | 145 |

Notes and Comments | 203 |

225 | |

List of Special Symbols | 235 |

Author Index | 237 |

241 | |

### Common terms and phrases

analytic Banach space bases basis for H basis for L*[–t Bessel sequence biorthogonal Boas bounded linear operator canonical product completeness radius complex exponentials complex numbers Corollary defined denote density disk entire function f(z equivalent example exists exponential type Fourier series function of exponential functional Hilbert space half-plane hence Hilbert space Hint inequality inner product integral interpolating sequence interval isomorphism Jensen's formula Lemma Let f Let f(z Levinson linear span nonharmonic Fourier series normed vector space orthogonal orthonormal basis Paley and Wiener Paley–Wiener space Paley–Wiener theorem Parseval's identity Pólya polynomial positive constants positive number Problem proof of Theorem Prove real axis real numbers result follows Riesz basis Riesz–Fischer sequence scalars c1 Schauder Schauder basis Section separable Hilbert space sequence f sequence of positive sequence of real sequence of scalars sequence of vectors space H Suppose Theorem 14 trigonometric system uniformly unique values zeros of f(z