## Linear Operators: Spectral operators |

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Page 1180

(66) sup y”(r) = |r!, a e B; y” e Yand that in consequence Corollary 22 is valid for

functions f(r, s) with values in

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

(66) sup y”(r) = |r!, a e B; y” e Yand that in consequence Corollary 22 is valid for

functions f(r, s) with values in

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

Page 1262

28 Let a self adjoint operator A in a

there exists a

Ar = PQr, are \), P denoting the orthogonal projection of S), on S). 29 Let {T,} be a

...

28 Let a self adjoint operator A in a

**Hilbert space**X, with 0 < A : I be given. Thenthere exists a

**Hilbert space**S, D \, and an orthogonal projection Q in Qi such thatAr = PQr, are \), P denoting the orthogonal projection of S), on S). 29 Let {T,} be a

...

Page 1773

APPENDIX

numbers, together with a complex function (-, -) defined on 9 × S3 with the

following properties: (i) (a, ar) = 0 if and only if a = 0; (ii) (ar, ar) > 0, a e \); (iii) (a +

y, ...

APPENDIX

**Hilbert space**is a linear vector space $) over the field op of complexnumbers, together with a complex function (-, -) defined on 9 × S3 with the

following properties: (i) (a, ar) = 0 if and only if a = 0; (ii) (ar, ar) > 0, a e \); (iii) (a +

y, ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

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adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero