## Linear Operators, Volume 2 |

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Page 1051

Statement ( i ) is

Statement ( i ) is

**evident**from Definition 1. Statements ( ii ) and ( iii ) are**evident**consequences of Definition 1 and of the formulae SexP ( x ) dx = Send ( Ux ) dx , Sen 9 ( ax ) dx 101 - SenQ ( x ) dx , which are valid for every ...Page 1347

This procedure has the

This procedure has the

**evident**advantage that it makes o ; ( :, 2 ) an entire function of the complex variable 2 ; but it has drawbacks which , though less**evident**, are nevertheless decisive . Suppose , for example , that we study the ...Page 1756

( B ) The uniqueness of the function V of the theorem is an

( B ) The uniqueness of the function V of the theorem is an

**evident**consequence of statement ( i ) . Moreover , statement ( 1 ) enables us to reduce the proof of the existence of the function V to the proof of the following statement .### 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 derivatives 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