## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1236

**boundary conditions**C ; ( x ) = 0 , j = 1 , ... , m , is said to be stronger i than the set B ( x ) = 0 , i = 1 , ... , k , if the boundary values B , are all linear combinations of the Cz . If each of two sets of**boundary conditions**is ...Page 1305

If B ( 1 ) O is not a

If B ( 1 ) O is not a

**boundary condition**either at a or at b ( so that , by Theorem 19 , the equation B ( A ) = 0 may be written ... A set of**boundary conditions**is said to be separated if it ( or , more generally , some set of boundary ...Page 1310

imposition of a separated symmetric set of

imposition of a separated symmetric set of

**boundary conditions**. Let In # 0. Then the**boundary conditions**are real , and there is exactly one solution ( t , 2 ) of ( 1-2 ) = 0 square - integrable at a and satisfying the q 9 boundary ...### What people are saying - Write a review

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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