## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 76

Page 1218

... ( c ) < and such that the

Proof . If the

o n d and thus the class of measurable functions having the required property is a

...

... ( c ) < and such that the

**restriction**of 1 to the complement of o is continuous .Proof . If the

**restrictions**flo , gd are continuous then so is the**restriction**( af + Bg )o n d and thus the class of measurable functions having the required property is a

...

Page 1239

Nelson Dunford, Jacob T. Schwartz. Conversely , let T , be a self adjoint

extension of T. Then by Lemma 26 , T is the

( T * ) determined by a symmetric family of linearly independent boundary

conditions B1 ...

Nelson Dunford, Jacob T. Schwartz. Conversely , let T , be a self adjoint

extension of T. Then by Lemma 26 , T is the

**restriction**of T * to a subspace W of D( T * ) determined by a symmetric family of linearly independent boundary

conditions B1 ...

Page 1471

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

70 , B ( f ) = B , G ( 1 ) + B2G2 ( t ) = 0 , Bi + B3 +0 , B1 , B , real , if + has ...

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self

adjoint

**restriction**T of T1 ( T ) is of the form B ( / ) = QG ( ) + 62G2 ( / ) = 0 , až + až70 , B ( f ) = B , G ( 1 ) + B2G2 ( t ) = 0 , Bi + B3 +0 , B1 , B , real , if + has ...

### 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