## Linear Operators: Spectral theory |

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Page 890

tne Hilbert space $q is infinite dimensional there is still an operational calculus

for a normal operator T with resolution of the identity E which is given by the

(vi) ...

tne Hilbert space $q is infinite dimensional there is still an operational calculus

for a normal operator T with resolution of the identity E which is given by the

**formula**(vi), but in this situation it is necessary to define the integral appearing in(vi) ...

Page 1112

+ Oil '12 fln-l,l an-l,2 • >„1 □ □ an-l,n Therefore, by Lagrange's expansion

biiYii = det(^)tr(^~1B), where yu denotes the cofactor of the element a{J of the

matrix A.

+ Oil '12 fln-l,l an-l,2 • >„1 □ □ an-l,n Therefore, by Lagrange's expansion

**formula**and Cramer's**formula**for matrix inverses, we have j det(A+zB)\I=0 = J £biiYii = det(^)tr(^~1B), where yu denotes the cofactor of the element a{J of the

matrix A.

Page 1363

basis for this

projection in the resolution of the identity for T corresponding to (Aj, Aj) may be

calculated from the resolvent by the

*->o £-0+ ...

basis for this

**formula**is found in Theorem XII.2.10 which asserts that theprojection in the resolution of the identity for T corresponding to (Aj, Aj) may be

calculated from the resolvent by the

**formula***t))f = Km lim — . f ' T)-«(A+ie; T)]/<M.*->o £-0+ ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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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