## Linear Operators: Spectral theory |

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Page 1236

0, i = 1,..., k, if the boundary values B, are all linear combinations of the C, . If each

of two sets of

**boundary conditions**C,(r) = 0, j = 1,..., m, is said to be stronger than the set B,(r) =0, i = 1,..., k, if the boundary values B, are all linear combinations of the C, . If each

of two sets of

**boundary conditions**is stronger than the other, then the sets are ...Page 1305

If B(f) = 0 is not a

the equation B(f) = 0 may be written as Bi(f) = B.(f), ... A set of

is said to be separated if it (or, more generally, some set of

If B(f) = 0 is not a

**boundary condition**either at a or at b (so that, by Theorem 19,the equation B(f) = 0 may be written as Bi(f) = B.(f), ... A set of

**boundary conditions**is said to be separated if it (or, more generally, some set of

**boundary conditions**...Page 1310

... G. Bade, Robert G. Bartle. imposition of a separated symmetric set of

actly one solution p(t, A) of (t–A) p = 0 square-integrable at a and satisfying the ...

... G. Bade, Robert G. Bartle. imposition of a separated symmetric set of

**boundary****conditions**. Let Jož # 0. Then the**boundary conditions**are real, and there is eaactly one solution p(t, A) of (t–A) p = 0 square-integrable at a and satisfying the ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

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