## Linear Operators: Spectral theory |

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Page 1180

(66) sup \y*(x)\ = \x\, xeB; and that in consequence Corollary 22 is valid for

functions f(x, s) with values in

with hardly any change in its proof, to the space of functions / with values in any

space ...

(66) sup \y*(x)\ = \x\, xeB; and that in consequence Corollary 22 is valid for

functions f(x, s) with values in

**Hilbert space**. Therefore, Corollary 23 generalizes,with hardly any change in its proof, to the space of functions / with values in any

space ...

Page 1262

28 Let a self adjoint operator A in a

there exists a

that Ax = PQx, x e Jp, P denoting the orthogonal projection of ^ on ^). 29 Let {Tn}

...

28 Let a self adjoint operator A in a

**Hilbert space**$» with 0 ^ A ^ / be given. Thenthere exists a

**Hilbert space**Jpx 2 §, and an orthogonal projection Q in §x suchthat Ax = PQx, x e Jp, P denoting the orthogonal projection of ^ on ^). 29 Let {Tn}

...

Page 1773

APPENDIX

numbers, together with a complex function (•, •) defined on §x§ with the following

properties: (i) (x, x) = 0 if and only if x = 0; (ii) (x, x) 2? 0, x e!g; (iii) (x+y, z) = (x, z) +

...

APPENDIX

**Hilbert space**is a linear vector space § over the field 0 of complexnumbers, together with a complex function (•, •) defined on §x§ with the following

properties: (i) (x, x) = 0 if and only if x = 0; (ii) (x, x) 2? 0, x e!g; (iii) (x+y, z) = (x, z) +

...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero