## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 72

Page 1297

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract "

see that the discussion leads us to a number of results about deficiency indices.

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract "

**boundary values**" introduced in the last chapter. We shallsee that the discussion leads us to a number of results about deficiency indices.

Page 1307

D2 are

)D^), /,ge3)(ri(T)). Proof. Let A be any

**boundary values**Clt C2 , Dl , D2 where C1 , C2 are**boundary values**at a and Dl ,D2 are

**boundary values**at b, such that (t/, g)-(/, rg) = CtfjCM-CMMi) +D1(i)D^)-Dl(f)D^), /,ge3)(ri(T)). Proof. Let A be any

**boundary value**for x. Since t is real, ...Page 1471

if t has no

two real

)-D2(f)Djg)-Fl(f, g), /, ge^T^)). By Theorem 2.30 and Corollary 2.31, a set of ...

if t has no

**boundary values**at b; while if t has**boundary values**at b, we may findtwo real

**boundary values**D1 , D2 for T2 at b, such that (T,/, g)-(/, rig) = D1(f)D2Tg)-D2(f)Djg)-Fl(f, g), /, ge^T^)). By Theorem 2.30 and Corollary 2.31, a set of ...

### 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