## Linear Operators, Part 2 |

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Page 1180

(66) sup jy"(.c)| = Ix], a: E B; 'OeYU and that in consequence Corollary 22 is valid

for functions f(a:, s) with values in

generalizes, with hardly any change in its proof, to the space of functions f with

values in ...

(66) sup jy"(.c)| = Ix], a: E B; 'OeYU and that in consequence Corollary 22 is valid

for functions f(a:, s) with values in

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

values in ...

Page 1262

28 Let a self adjoint operator A in a

there exists a

that Aa: = PQ.z', .2: e Q, P denoting the orthogonal projection of Si), on Q). 29 Let

...

28 Let a self adjoint operator A in a

**Hilbert space**Q) with 0 § A §I be given. Thenthere exists a

**Hilbert space**52), QQ, and an orthogonal projection Q in {)1 suchthat Aa: = PQ.z', .2: e Q, P denoting the orthogonal projection of Si), on Q). 29 Let

...

Page 1773

APPENDIX

numbers, together with a complex function (-, -) defined on $)><.§) with the

following properties: (i) (.z:,.r) = 0 if and only if .1: = 0; (ii) (.z,a:) g 0, 26$); (iii) (-1+9

, ...

APPENDIX

**Hilbert space**is a linear vector space 8;) over the field (D of complexnumbers, together with a complex function (-, -) defined on $)><.§) with the

following properties: (i) (.z:,.r) = 0 if and only if .1: = 0; (ii) (.z,a:) g 0, 26$); (iii) (-1+9

, ...

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### Contents

SPECTRAL THEORY | 858 |

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 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero