## Linear Operators: Spectral theory |

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Page 1236

B ; ( 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 setB ; ( 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 ( f ) = 0 may be written as B ( 0 ) ... 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 ( f ) = 0 may be written as B ( 0 ) ... 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 ) 9 = 0 square - integrable at a and satisfying the

imposition of a separated symmetric set of

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

**boundary conditions**are real , and there is exactly one solution y ( t , 2 ) of ( 1- 2 ) 9 = 0 square - integrable at a and satisfying the

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

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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