## Linear Operators: Spectral theory |

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Page 943

... sup | A(r1){A;(*)-A;(te)}y«(dO jeG \Jo = SUP | fc(r1)|*(*)-*(t»)|^(A) jeG JU □ h(trl)

Li(dt) = — h(t)fi(dt) Ju 2 Ju 2 Ju 2 Je 2 2 According to the first part of the theorem

there is a linear combination g of continuous

... sup | A(r1){A;(*)-A;(te)}y«(dO jeG \Jo = SUP | fc(r1)|*(*)-*(t»)|^(A) jeG JU □ h(trl)

Li(dt) = — h(t)fi(dt) Ju 2 Ju 2 Ju 2 Je 2 2 According to the first part of the theorem

there is a linear combination g of continuous

**finite dimensional**functions with ...Page 1092

(If there are only a finite number N of non-zero eigenvalues, we write A.n(T) = 0,n

>N). Then, for each positive ... domain and range. Note that if T has

.

(If there are only a finite number N of non-zero eigenvalues, we write A.n(T) = 0,n

>N). Then, for each positive ... domain and range. Note that if T has

**finite**-**dimensional**range, T = ET, where E is the orthogonal projection on the range of T.

Page 1146

Any

irreducible representations. This theorem shows that in studying

generality, confine ...

Any

**finite dimensional**representation of a compact group G is a direct sum ofirreducible representations. This theorem shows that in studying

**finite****dimensional**representations of a compact group G we may, without loss ofgenerality, confine ...

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### Contents

BAlgebras | 859 |

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 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