## Linear Operators: Spectral theory |

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Page 906

Unitary operators have a number of other characteristic properties. ... The

Hermitian operators are a subclass of B(&) which play a role in B($) much

resembling the role of the

numbers.

Unitary operators have a number of other characteristic properties. ... The

Hermitian operators are a subclass of B(&) which play a role in B($) much

resembling the role of the

**real numbers**as a subclass of the class of all complexnumbers.

Page 1251

In this section we shall show how the spectral theorem for self adjoint operators

may be applied to prove a number of results from the theory of moments and

shall begin our discussion ... Let mn, n = 0, 1, 2, . . ., be a sequence of

In this section we shall show how the spectral theorem for self adjoint operators

may be applied to prove a number of results from the theory of moments and

shall begin our discussion ... Let mn, n = 0, 1, 2, . . ., be a sequence of

**real****numbers**.Page 1921

V.l .7(410) Supremum, limit superior of a sequence of sets, (126) limit superior of

a set of

(96) Symmetric operator, definition, X.4.1 (906), XII.1.7 (1190) Symmetric ...

V.l .7(410) Supremum, limit superior of a sequence of sets, (126) limit superior of

a set of

**real numbers**, (4) of a set of**real numbers**, (3) Symmetric difference, (41 ),(96) Symmetric operator, definition, X.4.1 (906), XII.1.7 (1190) Symmetric ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero