## Linear Operators: Spectral theory |

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Results 1-3 of 83

Page 1297

The first

7\(t) is an adjoint (Theorem 10); therefore (cf. XII.1.6) $(7\(t)) is complete in the

) ...

The first

**norm**is the**norm**of the pair \f, TJ] as an element of the graph of ^(t). Now7\(t) is an adjoint (Theorem 10); therefore (cf. XII.1.6) $(7\(t)) is complete in the

**norm**Since the two additional terms in |/|2 are the**norm**of / as an element of Hn(J) ...

Page 1431

Because |gm|2 ->- 0, it follows that ]g£'|2 —0 for 0 ^ A; < n and therefore also that

By [*] this implies that \ang{n)\2 -»-0, and since |aB(*)|-1 is bounded by

hypothesis, |g„ '|2 -> 0- Thus {gm} converges to zero in the

closure of ...

Because |gm|2 ->- 0, it follows that ]g£'|2 —0 for 0 ^ A; < n and therefore also that

By [*] this implies that \ang{n)\2 -»-0, and since |aB(*)|-1 is bounded by

hypothesis, |g„ '|2 -> 0- Thus {gm} converges to zero in the

**norm**of (e) Theclosure of ...

Page 1699

by Lemma3.22, tpcFe is the limit in the

functions in C£°(L). Putting gj{x) = 0 for x in Ce—L, it follows from Definition 3.15

that (peFB is the limit in the

by Lemma3.22, tpcFe is the limit in the

**norm**of Hlv)(L) of asequence {gj} offunctions in C£°(L). Putting gj{x) = 0 for x in Ce—L, it follows from Definition 3.15

that (peFB is the limit in the

**norm**of HlP)(Ce) of the sequence {gf} of elements of ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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