## Linear Operators: Spectral theory |

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Results 1-3 of 84

Page 875

It will be

commutative B"-algebra & into the algebra C(A) of all continuous functions on the

structure space A of 3 is an isometric isomorphism of 3: onto all of C(A). It will also

be ...

It will be

**shown**that the homomorphism a → ~(~) (see Theorem 2.9) of acommutative B"-algebra & into the algebra C(A) of all continuous functions on the

structure space A of 3 is an isometric isomorphism of 3: onto all of C(A). It will also

be ...

Page 981

If H(T(f)) does not vanish identically for f in L1(R) then, as was

part of the proof of Theorem 3.11, there is a continuous character h on R with H.(T

(s)) =s, h(t)f(t)dr. fe L1(R). The converse part of Theorem 3.11 shows that such a ...

If H(T(f)) does not vanish identically for f in L1(R) then, as was

**shown**in the firstpart of the proof of Theorem 3.11, there is a continuous character h on R with H.(T

(s)) =s, h(t)f(t)dr. fe L1(R). The converse part of Theorem 3.11 shows that such a ...

Page 1161

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

Schwartz [2] for Euclidean space of three dimensions. It has recently been

by M. Paul Malliavin that spectral synthesis is not possible for all functions on the

...

That spectral synthesis is not possible for all functions in Lee 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 functions on the

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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