## Linear Operators: Spectral theory |

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Results 1-3 of 15

Page 1904

(See also Conver hull, Conver set, Conver space) Convex function, definition, VI.

10.1 (520) study of, VI.10 Convex hull, V.2.2 (414)

definition, V.1.1 (410) study of, V.1–2 Conyex space, locally, V.2.9 (417), (471)

strictly, ...

(See also Conver hull, Conver set, Conver space) Convex function, definition, VI.

10.1 (520) study of, VI.10 Convex hull, V.2.2 (414)

**Convex set**, II.4.1 (70)definition, V.1.1 (410) study of, V.1–2 Conyex space, locally, V.2.9 (417), (471)

strictly, ...

Page 1911

10.7 (323) Interior mapping principle, II.2.1 (55) discussion of, (83–85) Interior

point, I.4.1 (10) Interior of a set, I.4.1 (10) ... V.8.4 (440) Krein-Smulian theorem,

on convex closure of a weakly compact set, V.6.4 (434) on 3 closed

in ...

10.7 (323) Interior mapping principle, II.2.1 (55) discussion of, (83–85) Interior

point, I.4.1 (10) Interior of a set, I.4.1 (10) ... V.8.4 (440) Krein-Smulian theorem,

on convex closure of a weakly compact set, V.6.4 (434) on 3 closed

**convex sets**in ...

Page 1912

INDEX of £" in the bounded 3 topology, V.5.5 (428) separation of

V.2.10– 13 (417–418) Lower bound for an operator, XII.5.1 (1240) M Manifold,

closed linear, spanned by a set, II.1.4 (50) in a linear space, (36). (See also

Linear ...

INDEX of £" in the bounded 3 topology, V.5.5 (428) separation of

**convex sets**in,V.2.10– 13 (417–418) Lower bound for an operator, XII.5.1 (1240) M Manifold,

closed linear, spanned by a set, II.1.4 (50) in a linear space, (36). (See also

Linear ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

17 other sections not shown

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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