## Linear Operators: Spectral theory |

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Page 949

On the other hand, it has been

isomorphic with C(S), where S is a compact Abelian group, and also (Lemma 3)

that the continuous characters of S are of the form e^*. By Theorem 1.6, the set of

...

On the other hand, it has been

**seen**(Theorem 2) that AP is isometric andisomorphic with C(S), where S is a compact Abelian group, and also (Lemma 3)

that the continuous characters of S are of the form e^*. By Theorem 1.6, the set of

...

Page 977

R—-co 227 J 0 0 By substituting 6' for 6–p-H(t/2) and simplifying, it is

2n - G(u, v) - - (—ie”)" lim soni's ei(no'-(rs sin %)ds)'. 27. R—-co J 0 0 Now the

Bessel function J, of order n is defined by the equation I 27 J (z) - - eisng-3 sin "d6

; ...

R—-co 227 J 0 0 By substituting 6' for 6–p-H(t/2) and simplifying, it is

**seen**that I r2n - G(u, v) - - (—ie”)" lim soni's ei(no'-(rs sin %)ds)'. 27. R—-co J 0 0 Now the

Bessel function J, of order n is defined by the equation I 27 J (z) - - eisng-3 sin "d6

; ...

Page 1154

Since it is clear that X* = 2 x 2, what will be proved then, is that (i) Ž(*)(E) = c(2 × 2

)(E), E e X(2), for some constant c independent of E. This condition (i), as is

from Corollary III.11.6, is a consequence of the assertion that (ii) Ž(*)(4 × B) ...

Since it is clear that X* = 2 x 2, what will be proved then, is that (i) Ž(*)(E) = c(2 × 2

)(E), E e X(2), for some constant c independent of E. This condition (i), as is

**seen**from Corollary III.11.6, is a consequence of the assertion that (ii) Ž(*)(4 × B) ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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

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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