## Linear Operators: Spectral theory |

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Page 950

In the case R = ( — oo, +00), the

measure: in the case of a compact group, its existence and uniqueness was

proved in Theorem 1.1. The reader who is unfamiliar with

wish to ...

In the case R = ( — oo, +00), the

**Haar measure**may be taken to be Lebesguemeasure: in the case of a compact group, its existence and uniqueness was

proved in Theorem 1.1. The reader who is unfamiliar with

**Haar measure**maywish to ...

Page 1152

The existence of an invariant

countability was first shown by

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

Page 1154

a-compact group R and let Xbe a

XxX is a

locally compact and ff-compact, it has a

a-compact group R and let Xbe a

**Haar measure**in R. Then the product measureXxX is a

**Haar measure**in Rx R. Proof. Since the product group Ri2> = R x R islocally compact and ff-compact, it has a

**Haar measure**A(2) defined on its Borel ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 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 q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero