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

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Page 949

On the other hand , it has been

On the other hand , it has been

**seen**( Theorem 2 ) that AP is isometric and isomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma 3 ) that the continuous characters of S are of the form eidz .Page 1037

product clearly converges to zero for 1 = 2x it is readily

product clearly converges to zero for 1 = 2x it is readily

**seen**that the function P ( T ) is analytic for 2 # 0 and vanishes only for 2 in o ( T ) . It remains to show that if a # 0 , then qi ( T ) is continuous in T relative to the ...Page 1154

Since it is clear that Σ ( 2 ) Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) = c ( àx2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i ) , as is

Since it is clear that Σ ( 2 ) Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) = c ( àx2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i ) , as is

**seen**from Corollary III.11.6 , is a ...### What people are saying - Write a review

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### 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 Ly(R 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 unique unit unitary vanishes vector zero