## Linear Operators, Part 2 |

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Page 950

Every such group has a non-negative countably additive

defined on the Borel sets Z, finite on compact sets, positive or infinite on open

sets, invariant under translation, i.e., }.(a:+ E) = }.(E) for E in Z and at in R, and

which ...

Every such group has a non-negative countably additive

**measure**which isdefined on the Borel sets Z, finite on compact sets, positive or infinite on open

sets, invariant under translation, i.e., }.(a:+ E) = }.(E) for E in Z and at in R, and

which ...

Page 1152

The existence of an invariant

countability was first shown by Haar [1], and the question of uniqueness was first

discussed by von Neumann [17]. Other proofs of existence or uniqueness have ...

The existence of an invariant

**measure**on a group satisfying the second axiom ofcountability was first shown by Haar [1], and the question of uniqueness was first

discussed by von Neumann [17]. Other proofs of existence or uniqueness have ...

Page 1153

Since the

integration as developed in ('hapter III may be used as a basis for the theory

developed in Sections 8-4. In particular we should notice that the product group

RXR is a ...

Since the

**measure**space (R, Z, Z) is a 0-finite**measure**space the theory ofintegration as developed in ('hapter III may be used as a basis for the theory

developed in Sections 8-4. In particular we should notice that the product group

RXR is a ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma 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