## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 71

Page 942

Thus every eigenfunction of T , which

finite dimensional continuous function . Hence N is orthogonal to every

eigenfunction of T , except to those

Theorem X.3.4 ...

Thus every eigenfunction of T , which

**corresponds**to a non - zero eigenvalue is afinite dimensional continuous function . Hence N is orthogonal to every

eigenfunction of T , except to those

**corresponding**to a = 0. It follows fromTheorem X.3.4 ...

Page 1729

It should be evident from this last formula that much as in the

of the space 07 ( C ) , we may regard any point [ x1 , y ] for which 0 < x < 27 as

belonging , in a suitable sense , to the interior of C ; that is , to argue at such a ...

It should be evident from this last formula that much as in the

**corresponding**caseof the space 07 ( C ) , we may regard any point [ x1 , y ] for which 0 < x < 27 as

belonging , in a suitable sense , to the interior of C ; that is , to argue at such a ...

Page 1780

An equivalence class U of vectors u , will be said to

equivalence class V of vectors vp if there is a pair of vectors , one from U and one

from V ... Suppose that U and V are

u , EU .

An equivalence class U of vectors u , will be said to

**correspond**to anequivalence class V of vectors vp if there is a pair of vectors , one from U and one

from V ... Suppose that U and V are

**corresponding**equivalence classes and thatu , EU .

### What people are saying - Write a review

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

### Other editions - View all

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero