## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

Page 1902

Closed orthonormal system,

sphere, II.3.1 (59) Closure of a set, criterion to be in, I.7.2 (27)

...

Closed orthonormal system,

**definition**, IV.14.1 (357) study of, IV.14 Closed set,**definition**, I.4.3 (10) properties, I.4.4–5 (10) Closed sphere, II.4.1 (70) Closed unitsphere, II.3.1 (59) Closure of a set, criterion to be in, I.7.2 (27)

**definition**, I.4.9 (11)...

Page 1907

Essentially bounded,

separably valued,

of a function, by continuity, I.6.17 (23)

17) ...

Essentially bounded,

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

**definition**, III.1.11 ...**definitions**, (3) topology of, (11) Extensionof a function, by continuity, I.6.17 (23)

**definition**, (3) Tietze's theorem, I.5.3–4 (15–17) ...

Page 1921

T Tangent function,

properties, V.9.1 (445), V.9.3 (446), ... base and subbase for, I.4.6 (10) basic

3.2 (419) ...

T Tangent function,

**definition**, V.9.2 (446) examples, V.11.9–13 (458–459)properties, V.9.1 (445), V.9.3 (446), ... base and subbase for, I.4.6 (10) basic

**definitions**, I.4.1 (10) bounded 3' topology, V.5.3 (427) functional or T topology, V.3.2 (419) ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero