## Linear Operators, Part 2 |

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Page 1110

We saw in the course of proving

and by

case in ...

We saw in the course of proving

**Lemma**16 that the function det(I+T) of that**lemma**is continuous in T(cf. the remark which follows**Lemma**16). Thus, by (b)and by

**Lemma**11, to prove (f) in general we have only to prove (f) in the specialcase in ...

Page 1698

Using

by

(V), so that in case (a) we have shown that foqaf' is the limit in the norm of H“"(V) ...

Using

**Lemma**2.1, let up be a function in C§°(V) with 1p(.r) = 1 for .2 in K. Then,by

**Lemmas**3.22 and 3.10, fozpfl = 1p(fo<pf1) = limm__wzph,,_ in the norm of H"”(V), so that in case (a) we have shown that foqaf' is the limit in the norm of H“"(V) ...

Page 1733

Q.E.D.

neighborhood of the boundary of a domain with smooth boundary. This is carried

out in the next two

differential ...

Q.E.D.

**Lemma**18 enables us to use the method of proof of Theorem 2 in theneighborhood of the boundary of a domain with smooth boundary. This is carried

out in the next two

**lemmas**. 19**LEMMA**. Let o be an elliptic formal partialdifferential ...

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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