## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 73

Page 898

If we put E(d) = 0 when <5 n ff(T) is void, then

from Theorem 1 and

spectral measure associated, in

If we put E(d) = 0 when <5 n ff(T) is void, then

**Corollary**4 follows immediatelyfrom Theorem 1 and

**Corollary**IX. 3. 15. Q.E.D. 5 Definition. The uniquely definedspectral measure associated, in

**Corollary**4, with the normal operator T is called ...Page 1301

Proceeding inductively we see that v^(b) = 0, 0 ^ A; 2n — 1. However, as v0

satisfies an equation of order 2n, v0 must be identically zero. This contradiction

completes the proof. Q.E.D. 23

order ...

Proceeding inductively we see that v^(b) = 0, 0 ^ A; 2n — 1. However, as v0

satisfies an equation of order 2n, v0 must be identically zero. This contradiction

completes the proof. Q.E.D. 23

**Corollary**. Let r be a formal differential operator oforder ...

Page 1459

Q.E.D. 80

operator r is finite below zero. Proof. It is obvious from Definition 20 that t is

bounded below. Thus the present

Definition 25(b).

Q.E.D. 80

**Corollary**. A formally positive formally symmetric formal differentialoperator r is finite below zero. Proof. It is obvious from Definition 20 that t is

bounded below. Thus the present

**corollary**follows from**Corollary**7 andDefinition 25(b).

### 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