## 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 993

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. for almost

all m. It remains to be proved that the number oy is independent of the

. If f is in L1(R) n L.(R), f wanishes on the complement of V, and f(m) = 1 for m in ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. for almost

all m. It remains to be proved that the number oy is independent of the

**open set**V. If f is in L1(R) n L.(R), f wanishes on the complement of V, and f(m) = 1 for m in ...

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...

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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