## Linear Operators, Part 2 |

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Page 1236

-(.v) = 0, i = 1, . . ., k, if the boundary values B, are all linear combinations of the Cj

. If each of two sets of

**boundary conditions**C,(.z-) = 0, 7' = 1, . . ., m, is said to be stronger than the set B,-(.v) = 0, i = 1, . . ., k, if the boundary values B, are all linear combinations of the Cj

. If each of two sets of

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

If B(f) = 0 is not a

the equation B( f) = 0 may be written as B1(f) ... A set of

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 B1(f) ... A set of

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

**boundary conditions**...Page 1310

Then the

of ('r—}.)<p = 0 square-integrable at a and satisfying the

, and exactly one solution 1p(i, Z) of (r —}.)1p = 0 square-integrable at b amt ...

Then the

**boundary conditions**are real, and there is exactly one solution <p(t, 1.)of ('r—}.)<p = 0 square-integrable at a and satisfying the

**boundary conditions**at a, and exactly one solution 1p(i, Z) of (r —}.)1p = 0 square-integrable at b amt ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma 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