## Linear Operators: Spectral theory |

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Page 906

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

between unitary operators and complex numbers of unit modulus, Hermitian

operators and

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

between unitary operators and complex numbers of unit modulus, Hermitian

operators and

**real numbers**, and positive operators and positive numbers is ...Page 1744

... theorem be satisfied. Let x be any angular sector in the compler plane

including the positive real aris and the countable set of

(i) there eacists a

is in ...

... theorem be satisfied. Let x be any angular sector in the compler plane

including the positive real aris and the countable set of

**real numbers**a (V). Then,(i) there eacists a

**real number**K such that |R(Å; V)fter) s K|f|, fe L2(I), A # 2; (ii) if fis in ...

Page 1921

... I.8.1 (32) of

(49) topological space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, (

419) weak* topology, (462) 3 and 3: “topologies in 3", (419) Total boundedness, ...

... I.8.1 (32) of

**real numbers**, (11) study of, I.4–8 topological group, definition, II.1.1(49) topological space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, (

419) weak* topology, (462) 3 and 3: “topologies in 3", (419) Total boundedness, ...

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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