## Linear Operators: Spectral operators |

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Results 1-3 of 84

Page 1900

Almost periodic functions,

IV.15 (379)

Almost uniform (or pu-uniform convergence)

Almost periodic functions,

**definition**, IV.2.25 (242) space of, additional properties,IV.15 (379)

**definition**, IV.2.25 (242) remarks concerning, (386–387) study of, IV.7Almost uniform (or pu-uniform convergence)

**definition**, III. 6.1 (145). (See also ...Page 1907

Essentially bounded,

separably valued,

(238) further properties, IV.15 (374) study of, IV.3 Euler-Gauss, hypergeometric ...

Essentially bounded,

**definition**, III.1.11 (100–101) E-, X.2 (899) Essentiallyseparably valued,

**definition**, III.1.11 (100–101) Euclidean space,**definition**, IV.2.1(238) further properties, IV.15 (374) study of, IV.3 Euler-Gauss, hypergeometric ...

Page 1921

T Tangent function,

properties, V.9.1 (445), V.9.3 (446), V.11.10–11 (459) Tangent functionals,

analytic ...

T Tangent function,

**definition**, V.9.2 (446) examples, V.11.9–13 (458–459)properties, V.9.1 (445), V.9.3 (446), V.11.10–11 (459) Tangent functionals,

**definition**, V.9.4 (447) Tarski fixed-point theorem, I.3.10 (8) Taylor expansion foranalytic ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero