## Linear Operators: Spectral theory |

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Results 1-3 of 8

Page 1134

... so that E

then it

. .] belongs to the range of the projection Ea. Thus (Tnf, f) = cn{

... so that E

**is**in &. If (Aq, At)**is**an interval complementary to the closed set C,then it

**is**plain from Theorem 4 that Ex ... T"f=[cnx+g[n\gTM,...],. where [g^1', gŁn), .. .] belongs to the range of the projection Ea. Thus (Tnf, f) = cn{

**b-a**). Since T**is**...Page 1264

Then f(An) -*□ f(A) strongly for each bounded function / of a real variable which

is continuous except on a closed set C ... Principle, Heisenberg) Let A and B be

self adjoint operators in Hilbert space such that 2)0 = ^)(AB) n ^(

Then f(An) -*□ f(A) strongly for each bounded function / of a real variable which

is continuous except on a closed set C ... Principle, Heisenberg) Let A and B be

self adjoint operators in Hilbert space such that 2)0 = ^)(AB) n ^(

**BA**)**is**dense.Page 1885

NOTATION INDEX 21 (955) (a, 6], etc. (4) A(a) (522) A(av . . ., ak) (522) .4(a) (685

) A„ (619) A">(I) (1652) A<» (I) (1662), (1663) A(D) (242) A(n) (661) A- (/) (1280) A

(T, n) (661) AC(I) (242) AP (242) A (11)

NOTATION INDEX 21 (955) (a, 6], etc. (4) A(a) (522) A(av . . ., ak) (522) .4(a) (685

) A„ (619) A">(I) (1652) A<» (I) (1662), (1663) A(D) (242) A(n) (661) A- (/) (1280) A

(T, n) (661) AC(I) (242) AP (242) A (11)

**ba**(**S**, 2)**ba**(**S**,Z,X) (240) (160) bs bi- bi\t ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

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