## Linear Operators: Spectral theory |

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Page 873

Let *Jl A be the set in of all 9JiA with XeA. To see that A is dense in suppose the

... To see that <5_1 is continuous, i.e., to see that 6 maps

Let *Jl A be the set in of all 9JiA with XeA. To see that A is dense in suppose the

... To see that <5_1 is continuous, i.e., to see that 6 maps

**open sets**onto**open****sets**note first that**open sets**of the form (/?) are mapped into sets of the form (a) ...Page 1151

R = Utoi^n- ^e observe that if A and B are disjoint closed subsets of R and if n is

an integer, then there is an

This is true since for each p e A n Kn there is an

...

R = Utoi^n- ^e observe that if A and B are disjoint closed subsets of R and if n is

an integer, then there is an

**open set**U Q R such that A n Kn Q U and U n B = <f>.This is true since for each p e A n Kn there is an

**open set**U(p) such that p e U(p)...

Page 1660

... other points) as the intersection with C of an

the points with which x is identified. It is apparent that by this set of identifications

C becomes topologically equivalent to the Cartesian product of n replicas of the ...

... other points) as the intersection with C of an

**open set**of En containing x and allthe points with which x is identified. It is apparent that by this set of identifications

C becomes topologically equivalent to the Cartesian product of n replicas of the ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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### Common terms and phrases

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