## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

### From inside the book

Results 1-3 of 85

Page 1669

Let M : 11 +1 , be a

Let M : 11 +1 , be a

**mapping**of l , into 1 , such that ( a ) M - 1C is a compact subset of I , whenever C is a compact subset of I , ; ( b ) ( M ( - ) ) , e Co ( 11 ) , Then ( i ) for each g in Co ( 12 ) , po M will denote the function ...Page 1671

If F corresponds to the function f , we have k ( Fo M - ) ( 0 ) = F ( po M ) = 5+ ( x ) p ( M ( x ) ) dx = St ( M - 1 ( x ) ) p ( x ) J ( x ) dx , J denoting the absolute value of the Jacobian determinant of the

If F corresponds to the function f , we have k ( Fo M - ) ( 0 ) = F ( po M ) = 5+ ( x ) p ( M ( x ) ) dx = St ( M - 1 ( x ) ) p ( x ) J ( x ) dx , J denoting the absolute value of the Jacobian determinant of the

**mapping**x → M - 1 ( x ) ...Page 1707

Hence , by Lemma 3.41 , tota is a continuous

Hence , by Lemma 3.41 , tota is a continuous

**mapping**with a continuous inverse of H k + P ) ( C ) onto H * ) ( C ) , for all k between oo and too . Let Ve and Űk be the norms of the map to + : H6k + P ) ( C ) → H ( C ) Hľk and of its ...### 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 analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero