Linear Operators: Spectral theory |
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Page 891
scalar function f 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 .
scalar function f 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 X 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 ...
It is plain from Plancherel's theorem that X 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 1922
Total space of functionals , definition , V.3.1 ( 418 ) Total variation of a function , III.5.15 ( 140 ) of a set function , III.1.4 ( 97 ) . ( See also Variation ) Totally ordered set , 1.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ...
Total space of functionals , definition , V.3.1 ( 418 ) Total variation of a function , III.5.15 ( 140 ) of a set function , III.1.4 ( 97 ) . ( See also Variation ) Totally ordered set , 1.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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additive Akad 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