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

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Page 875

It will be

It will be

**shown**that the homomorphism x + x ( s ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 1 ) of all continuous functions on the structure space 1 of X is an isometric isomorphism of X onto all of C ( 4 ) ...Page 981

If H ( T ( ) ) does not vanish identically for f in L ( R ) then , as was

If H ( T ( ) ) does not vanish identically for f in L ( R ) then , as was

**shown**in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H ( T ( 1 ) ) = Sx h ( x ) f ( x ) dx , feLi ( R ) .Page 1161

That spectral synthesis is not possible for all functions in Lo was

That spectral synthesis is not possible for all functions in Lo was

**shown**by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been**shown**by M. Paul Malliavin that spectral synthesis is not possible for all ...### What people are saying - Write a review

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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