## Linear Operators: Spectral theory |

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Page 891

scalar

scalar

**function**with respect to the operator valued set**function**E. In the present chapter we shall only integrate bounded**functions**; and so the following discussion of the integral will be restricted to that case .Page 1178

It is plain from Plancherel's theorem that K is a bounded mapping of the space L , of scalar - valued

It is plain from Plancherel's theorem that K is a bounded mapping of the space L , of scalar - valued

**functions**into the ... Let M be the mapping in L ( 12 ) which maps the vector - valued**function**whose nth component has the Fourier ...Page 1645

If we let 4 be its closure , we find that D ( 1 ) contains nondifferentiable

If we let 4 be its closure , we find that D ( 1 ) contains nondifferentiable

**functions**. ... we should be able to define One On for every**function**, differentiable or not , and irrespective of whether On Of belongs to L2 ( E2 ) or not .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 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