## Linear Operators: Spectral theory |

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Page 873

Let ~4. be the set in 24 of all SURA with 2 e A. To see that .44 is dense in .4

suppose the contrary and let {{UR r ... Now, the complete regularity of A enables

us to see that every

Let ~4. be the set in 24 of all SURA with 2 e A. To see that .44 is dense in .4

suppose the contrary and let {{UR r ... Now, the complete regularity of A enables

us to see that every

**open set**in A is a union of sets of the form (3), for let G be a ...Page 1151

We observe that if A and B are disjoint closed subsets of R and if n is an integer,

then there is an

since for each p e A o K, there is an

...

We 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 C R such that A n K, C U and U n B = 4. This is truesince for each p e A o K, there is an

**open set**U(p) such that p e U(p) and U(p) n B...

Page 1660

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

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

identifications C becomes topologically equivalent to the Cartesian product of n

replicas of ...

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

**open set**of E" containing a and allthe points with which as is identified. It is apparent that by this set of

identifications C becomes topologically equivalent to the Cartesian product of n

replicas of ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero