## Linear Operators: Spectral theory |

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Page 1236

Bi ( x ) = 0 , i = 1 , . . . , k , if the boundary values B ; are all linear combinations of

the Cy . If each of two sets of

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

the Cy . If each of two sets of

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

If B ( t ) = 0 is not a

, the equation B ( t ) = 0 may be written as B ( 1 ) ... A set of

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

If B ( t ) = 0 is not a

**boundary condition**either at a or at b ( so that , by Theorem 19, the equation B ( t ) = 0 may be written as B ( 1 ) ... A set of

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

**boundary conditions**...Page 1310

imposition of a separated symmetric set of

the

- 2 ) = 0 square - integrable at a and satisfying the

imposition of a separated symmetric set of

**boundary conditions**. Let Il # 0 . Thenthe

**boundary conditions**are real , and there is exactly one solution o ( t , 2 ) of ( 1- 2 ) = 0 square - integrable at a and satisfying the

**boundary conditions**at a ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero