## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

Page 898

E is the resolution of the

complex numbers, then where Ts is the restriction of T to E(d)Sj. Proof. The first

statement follows from Theorem l(ii). Now for f ^ d it is seen from Theorem 1.1 ...

E is the resolution of the

**identity**for the normal operator T and if d is a Borel set ofcomplex numbers, then where Ts is the restriction of T to E(d)Sj. Proof. The first

statement follows from Theorem l(ii). Now for f ^ d it is seen from Theorem 1.1 ...

Page 920

Let E and £ be the resolutions of the

Corollary 2.7 it is seen that £ = VEV1 and hence that F(T) = VFlTjV-1 for every

bounded Borel function F. The mapping W = 0 V of § onto L2(e„, /I) is clearly an

isometry ...

Let E and £ be the resolutions of the

**identity**for T and T respectively. FromCorollary 2.7 it is seen that £ = VEV1 and hence that F(T) = VFlTjV-1 for every

bounded Borel function F. The mapping W = 0 V of § onto L2(e„, /I) is clearly an

isometry ...

Page 1717

By induction on \Jj\, we can readily show that a formal

dJ>dJ* + 2 CjraAx)^, \j\ <<j1\ + <Jt\ with suitable coefficients Cj j , holds for every

function Cin CJj°(/0). Making use of

By induction on \Jj\, we can readily show that a formal

**identity**(1) 8JiC(x)F* = C(x)dJ>dJ* + 2 CjraAx)^, \j\ <<j1\ + <Jt\ with suitable coefficients Cj j , holds for every

function Cin CJj°(/0). Making use of

**identities**of the type (1), we may evidently ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

31 other sections not shown

### Other editions - View all

### 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