## Linear Operators, Part 2 |

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Page 1100

matrix with the same eigenvalues as A, the statement (3) follows from the

inequality Art»-<v1>. I/'1». ... Since the linear functional t~r is continuous on C1,

and since, as we have observed in the paragraph

AB is a ...

matrix with the same eigenvalues as A, the statement (3) follows from the

inequality Art»-<v1>. I/'1». ... Since the linear functional t~r is continuous on C1,

and since, as we have observed in the paragraph

**following Lemma**9, [A, B] —>AB is a ...

Page 1696

By Lemma 14 there is a sequence {Fm} of elements of D(I ), each of which has a

carrier which is a compact subset Cm of I ... it

3.12 that there is a unique extension G of F to a distribution in D,,(D) such that the

...

By Lemma 14 there is a sequence {Fm} of elements of D(I ), each of which has a

carrier which is a compact subset Cm of I ... it

**follows from Lemmas**13, 3.43 and3.12 that there is a unique extension G of F to a distribution in D,,(D) such that the

...

Page 1733

... it

present

to use the method of proof of Theorem 2 in the neighborhood of the boundary of a

...

... it

**follows**that |A"1(foS-—/)](,,°) is uniformly bounded in A, from which thepresent

**lemma follows**, as has been shown above. Q.E.D.**Lemma**18 enables usto use the method of proof of Theorem 2 in the neighborhood of the boundary of a

...

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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